Many forms of Priesthoods exist today and in the past. A very common system is a division of sacred offices.
Usually there is the ritualist, the seer, and the poet/singer, and often a fourth type of someone who knows the lore and rituals well and oversee the rituals to prevent or correct any errors.
Among the Keltoi/Galatoi (Celts/Galatians) this division can be seen in the division between the Druids who oversaw the rituals, and served as advisors; the Vates who were seers, and who carried out rituals; and the Bards who knew the songs, and epics.
The Romans had similar divisions particularly with the Pontifices who oversaw the priesthoods, the Flamines who carried the rituals out, and the Augurs who served as diviners.
The Vedics had the Brahmans who oversaw the rituals and corrected errors; the Hotri who presided and invoked the deities; the Adhvaryu who prepared the site, and and carried out the sacrifice; and the Udgatri who chanted/sang the hymns.
Such a division is seen amongst the Hellenes as well, with the Hiereus who oversaw the rituals, ensuring the everything is prepared and performed properly and invoked the Gods, the Mantis or seer and diviner, and the Rhapsode who sang and who kept the myths and sacred poetry.
In ancient China, the Zhu (Invoker or Priest), the Wu (Shaman), and the Diviner ran the rituals and assisted the Wang (King) or Huangdi (Emperor) to channel the Shen (Gods and Spirits) and Guei (ghosts of ancestors) for guidance and to keep the sacred order, and in his Hieros Gamos with rain nymphs and goddesses..
In Daoism, the further broke down into specialists, as today there are Guagong (High Priest or Ritual Master) who invokes the Shen and Guei, and by symbolic acts, links man with the spirits. He is assisted by two other Ritual Masters. The Dujiang or Chief Cantor who is also intimately familiar with the rituals, and who leads the sacred chants. The third Ritual Master is the Jianzhai (Inspector of Feasts) who masters the regulations of ritual, and corrects errors, to keep the ritual on track.
These divisions are logical and make considerable sense. They provide a needed division of labor in religion as elsewhere. Not everyone is skilled at all sacred skills. Modern Priests, especially in the Monotheist religions is “on thing for everyone” but this is because they are primarily ritualists. As elders (presbyteroi, the root of “priest”) they also provide counsel.
The nearest example in a pagan sense, would be the Kannushi (Shrine Priest, male or female) who invokes the Kami (spirits or numina/gods), and provide blessings and exocisms. They are ranked by seniority, with junior clerics wearing blue hakima pants, and the senior cleric wearing purple ones.
Ancient priests of various types had more functions, and as a result they are divided up into different orders. Those who knew the rituals well enough to perform them served as priests. (And as Burkert points out, anyone who knew the cutoms involved could perform rituals at home or in sanctuaries if no priest was present). Seers or Manteis and Sibyls spoke for deities and observed the auspices and omens, to advise on actions, and helped with divination techniques. Rhapsodes learned poems and songs, and performed them in rituals, and in other situations.
Thus people with certain skills could specialize in what they did best, and probably provided better service in what they did do. One did not try to master all these areas of service at the same time, and perhaps only do a passing (or even a miserable) job at one or more function. One also would not be intimidated to assume the office of priest because one did not perform a sacred function well, or one disbelieves in, say, divination.
I believe that such division of labor would be a wise one to follow, and thereby open up sacred offices to more participants.
Other options would be to look at minor orders of priesthood or sacred services.
In Vedism, the various Priests are served by assistants, minor priests. At major rituals, you had up to 16 priests working at the same time, the four main priests, and each had three minor priests assisting them.
The Hotri was aided by the Maitravaaruna, aided in officiating the ritual and carried a sacred cup. The Achaavaaka aided in the invocation of the deities, and the graavastut helped with the soma pressing, and praised the sacred mortar.
The Adhvaryu was assited by the Pratisprasthaar, who held the milk jugs used in the soma ritual. The Neshtri assisted the sacrificer’s wife, and prepared and held the soma vessel. The Unnetri priest drew out and poured the soma into the vessels for the Adhvaryu who then poured it into the fire.
The Brahmans were aided by the Braahmanaacchansin who helped cut the soma plant, and covered up things. The agniindra kindled the sacrificial fire, while the Potri or purifier and carried the soma vessel.
The Udgatri had the Presstaava who chanted the introductory eulogy, and the prelude of the samman hymns. He also praised, sang and chanted with the Udgatri. The Pratihartri began to sing, especially in the final stanzas of the hymns to increase their effectivenss. There was also the Subrahman who helped sing the praises of the priests to the deities.
In Shinto, the Kannushi is aided by the Miko. They assist in rituals, and provide sacred dances. In ancient times, they served as female prophetic shamans and oracles, and to this day help with a lot oracle in the Jinja or shrine. They also staff shrine shops, and help sweep and maintain the grounds.
In Taoism, there are also lesser priests who aid in rituals. The Shixiang or Incense Attendant, (who holds the ancient title of Miazhu, or Shrine Priest). He arranges the incense burner, keeps the incense burning, and keeping the ritual area clean and organized so the Ritual Masters can focus on their duties.
The Shideng or Lantern Attendant keeps lanters and candles ready and in the prescribed order and type for the ritual. They keep the lanterns burning bright, and light them at night, and blow them out in the morning, while also keeping the ritual area and offering altar bright and magnificently lit.
The Shijing or Bell Attendant cleans scroll covers clean, organizes and orders the scriptures he gathered, and exhibits them properly in the ritual space for the use of the Ritualists. He also harmonizes voices, sets example, and keeps the spirits happy with song, after setting up the chanting scriptures for everyone to read, and helps sing the odes. Prior to ritual he prepares the ritual space (as the Adhvaryu does in Vedism), inspecting everything used, and after wards, cleans up the space, and cleans it up, while keeping the profane from the ritual altar.
In Ancient Hellas, there were similar minor orders. The Neokoroi kept the sanctuary clean , and assisted the Hiereus. The Neokoros served as caretaker or sacristan of the sanctuary. The Hieropoioi organized the sacrifice, including obtaining the oblation to be sacrificed, and executed the oblation. Afterwards, they sold skins, distributed unconsumed food, and sold whatever was not distrbuted. The Epimeletai or Hierotamiai oversaw the finances of the sacrifices.
Others assisted in the procession or Pompe, such as the Basket Bearer, the Lustrophoros or Water Bearer, the Fire Bearer, Bowl Bearers, Bough Bearers, and the Kistephoroi and Liknophoroi of the Dionysian festivals. Musicians and dancers also assisted in the ritual.
Other specialist priests oversaw the Mysteries, such as the Hierophant who introduced participants to the Holy, the Dadouchos or torch bearers, the Hierokeryx or Sacred Herald, Priestesses, and lesser purifying priests and priestesses who aided the potential initiate in preparing for the ritual, and the Mystagogues.
Christian Priests, especially of High Church varieties are divided into a hierarchy of Major Orders: Bishops or regional overseers, Priests/Presbyters who preside over the ritual, and the Deacon who helps the Priest, and who administers services. The Subdeacon (now eleminated) aided with the readings of the epistles, carried gospel after the deacon or Priest read it, aided Priests and or deacons in setting up the altar.
They are aided by Minor Orders, which Priests and Deacons had to pass through as they were trained and educated into their Major Roles. Others served in these Orders and had no determination to go further. They did not have the same vows of the Major Orders and so were not as onerous. Today, in Roman Catholicism, these Minor Orders are elminated and became Lay Ministries.
The highest ranked was the Acolytes who administers communion, celebrated the minor ritual of Exposition of the Blessed Sacrament, purified vessls, and had priority in leading blessings and celebrations if no Priest or Deacon is available.
Below the Acolytes are the Exorcists who exorcise the catechumens in Baptism (some Priests are set aside as Exorcists to deal with demons).
The Lector read the Old Testament and Epistles, Deacons (or if no Deacons are around, the Priest) alone could read Gospels. Priests or other Presiders should not be distracted by the need to make the readings. If there is no Cantor, they chant or recite the Psalms. If no Deacons or Cantor is available, they read the general intentions and Prayers of the faithful.
Cantors are musicians who sing, and lead the choir.
Finally there is the Ostiarius or Ostiary (Porter or Doorman or Gatekeeper) who opens and closes the doors to the sanctuary, guards the church, and keeps the unbaptized from the Eucharist. They also guard, open and close the doors of the Sacristry, Baptistry and other parts of the church. Also known as a Sacristan, who cared for the Sacristry, the vessels, vestments, and linens in it (and clean them). As Sexton, the Sacristan also cared for the buildings and grounds.
Altar Servers also provide assistant to the clergy, as laypersons. They fetch and carry, ring bells, carry items in the processions, others serve as Thurifers. They hold the missal to free the Priest’s hands during the Opening Prayer, carry gifts of bread and wine to the Priests, prepare the chalices, administers water to the Priest as he washes his hands, rings bells during the Celebration of the Eucharist. They serve to allow the Priest to focus on the ritual itself without distractions of having to do certain functions.
The Thurifer holds the Thurible or Censer while the Priest blesses the incense. They keep the thurible filled with coal, and that the coal is lit. They also add incense as needed during the ritual, and carry it in procession. The Thurifer may be aided by yet another server, who carries the Boat, which contains fresh incense.
These minor orders provide less demanding roles which do not require the same commitment as the major priests, and provide an outlet for people who wish to assist in worship. They also provide training for priests of higher orders, in stages, as they progress up the hierarchy. Some of these have clear similarities to ancient minor orders, and could be considered for our use today.
I have visited pagan rituals where the officiating Priest or Priestess could certainly have used a few altar servers to keep the incense fed, and other minor tasks that disrupted their performance of the ritual.
I also know of some who wish to live a life dedicated entirely to the deities in a manner allowing contemplation or devotion continuously. The most similar role would be that of monastic orders. There is ancient precedence for this, as the Pythagoreans created communal societies focused on virtuous living and religion, and contemplation. There were also the mysterious Therapeutae, who some argued were influenced by Buddhism and a possible origin of their name is a corruption of Theraveda. Monastics were found in the Greco-Bactrian kingdoms under the influence of Greco-Buddhism. While most Priests lived a part time existence, some forms of ancient religion had permanent priests such as the Brahmins and Druids. Contemplation and Meditation on the Holy and Good was also a feature of the philosophers of the Academy and Lyceum, while Iamblichus and others sought to live by Pythagorean principles. Ancient Nympholepts also lived as Eremites and Cenobites to contemplate and commune with the Nymphs, much as Taoist hermits and monks do, and the Shugendo Yamabushi and Shukenja do in Japan, communing with their nature spirits.
I could easily imagine a sort of Pagan Jesuit Order, dedicated to Athena. The intellectual focus, and military discipline of the Jesuits and their contemplative life fit well with Her. While something like the Knights Templar or the Japanese Sohei and Chinese Shaolin would fit well with both Athena and Ares.
There were other sacred functionaries as well. The Exegetes were official interpreters of both Sacred and Secular Law, and advised people needing guidance. Many ancient Philosophers provided counselling both in ethics, and early forms of psychological counselling. Many of them lived in the homes of citizens as advisors and some sort of chaplain, while others advised rulers.
These sorts of ministers, addressing the needs of the people, could be established today as a form of semi-Priestly specialists, or a bona fide member of the clergy, as oft-times these functions are associated with the Priesthood in our modern society. There is also precedent for this function, as the Magi of Indo-Iranian Persia, and the Druids of the Celts were priestly philosophers and advisors, and were considered for their wisdom by ancient Greeks and Romans, and Magos/Magus originally had such a connotation as Graf explains in his book Magic in the Ancient World. Only later did they gain a reputation for magic. Even in folklore and fiction, Mages and wizards are considered and depicted as very wise counsellors, whether we talk about Merlin or Gandalf, and even then there is a sense of holiness about these figures.
Vedics and Hindus took these advisory priests and holy men to a degree of specialization not normally seen. The Purohita was a family priest, chaplain and advisor, while the Guru was a godfather like mentor similar to a Godparent, Sunday School teacher or Cathechism teacher, preparing youths for initiation into adulthood, and advised and mentored the student for life. The Aachaarya was a spirtual guide or teacher, and who initiated the child, taught them the Vedas, and the laws of sacrifice and the Mysteries.
Rishis were similar to Rhapsodes, singing sacred hymns, and received direct inspiration, and composed the hymns of the Vedas. The Kavi were wise sages, prophets and singers, who kept the lore and epic tales.
The Mantrim knew the sacret texts, and were also wise men, and even developed a reputation for enchanting and conjuring, much like the Artharvan, a later form of priest who healed and performed spells like a Classical Goes or Thaumaturge while also providing counsel, much like the classic Wizard or Magus.
In Taoism, Wu or wizards and magicians provide exorcisms, and talismans for worshippers, and are considered part of the Taoist clergy. Miko retain aspects of their old shamanistic functions, selling protective talismans, and aiding in divination at the Shrines.
These are all various divisions of labor, training hierarchies, and other sacred functions in religions from the ancient world, and in surviving pagan/non-Abrahamic religions of this day. Much of ancient Classical religion and its practices, from the offices of Pontiff, down to simple things like lustral fonts at the entrance of sanctuaries, and Priests stepping off on the right foot when entering the sanctuary, are all inheritances in modern Christianity, especially Catholicism and Orthodoxy. Some of their orders may come from the State religion of Rome itself, just as many titles and usages, and canon law come from the Romans.
Also, while most ancient priests did not lecture or sermonize, at least during ritual itself, no doubt, being respected people, were relied on for advice and interpretation even if not officially assigned such functions. However, in attempts to compete and survive, we begin to see ancient Priests also providing such sermons and guidance during services in the late period, while amongst the Vedics and Celts, priests such as Druids and Brahmins always had such functions. While Taoist priests to this day give sermons and guidance to their faithful.
Such practices encourage personal participation in religious life and clergy, and aid in training, and should, in my opinion, be studied as we consider today ways to modernize and update ancient practices as Reconstructionists. Many of these have precedence in ancient times, and help us develop a modernized religion with ancient DNA.
I would also suggest these are models we can look to to create religions that provide for the spiritual needs of the people who follow it, and help cement the chances of our survival as a faith in the modern world. Many of the successful and still surviving ancient religons have such divisions, and it is one reason why they still exist, despite pressures from Western Monotheisms.
We should also review carefully the suggestions made by the Blessed Emperor Julian in reforms he wished to implement, had he survived to do so rather than dying in the Persian deserts. Many of those reforms make much sense, and if implemented today would strengthen ourselves. While these are not practices of 5th Century Athens, or 1st Century Rome, they are expressions of our religious traditions, as the religion evolved, and were attempts to remedy weaknesses apparent at the time in the face of the Monotheisms which we still face today.
Finally, I would recommend that some sort of equivalent of seminarian training in rituals, laws, myths, and ethics would be wise for at least major orders of Priesthoods. They would certainly help our reputations as serious religions rather than a bunch of self-proclaimed Priests, or High Priests. If one adds in apologetics, theological and philosophical training, responding to criticisms and theological attacks would become easier, and strengthen the intellectual supports of our faiths. Some sort of disciplinary structure, whether by ostracism or what not, by the community, religious orders and organizations, would help restrain bad behavior by priests. A real threat of being defrocked might prevent problems with priests and priestesses who engage in unethical or fraudulent behaviors.