The Priest, originally appearing in Palladium's fantasy game, returns in RIFTS with the supplement wherein multiple divine pantheons are statted up for use as NPCs. The Priest appears, adapted for the new game, but otherwise is the same Occupation as its Fantasy counterpart: to be the god's agent on that plane of existence, in that locality, and fulfill the god's agenda. To this end, the Priest is no different from the Witch, and much of what I said with regard to Witches applies here.
The big difference is that the Priest is the product of an institution, and therefore is an Occupation that only arises amongst communities that achieve a given threshold of economic and socio-political development, something that commonly coincides with the transition to agriculture and the beginnings of a city-centric sedentary pattern of settlement and the rise of a hierarchical oligarchy. Furthermore, be the Priest or his institution fair or foul, his is the very definition of a legitimate profession; priesthoods are up there with warriors and whores as the earliest of professions to arise in Civilization.
For the player, this means that--regardless of what happens after that point--your man began as part of a sacred institution and learned from a community of fellow priests. The magic you wield is a gift from the god that your man serves; it's an investment, and unless your patron is a God of Magic sort you likely have no fucking idea how magic works or why your powers actually work the way that they do. You're in the same position as a Shaman, but you have the advantage of a large institutional infrastructure to work with; you also have the responsibility to that same organization and can be called upon to act for the benefit of another priest, so this is a two-edged sword.
For the Game Master, Priests are no-brainers to include in a campaign regardless of any other genre elements you're throw into your crucible. Along with Witches, Mystics, Shaman, and other folks of similar levels of easy adaptability you've got ready-made world-building when you allow Priests into your game and you should take full advantage of that fact. The specifics of the Priest will vary greatly not only by the patron god itself, but also by how that specific priesthood organizes itself and execute its patron's agenda; a priesthood devoted to a public outreach program will not have the same sort of culture that one--even one devoted to the same god--organized to hunt down enemies of the god. Exploit this.
Outside of specific milieu such as the Coalition states, or similiar kill-all-magicians societies, you're going to have a priesthood of some sort due to gods being real and active in the universe. You might as well make that work for you, both as a player and as a Game Master. Enjoy.