Ok, these are the classes (as far as I understand them) that, as part of their core, they are devout followers of their deity. I have them listed from what I see as "caster centric" to "melee centric".
Caster centric
Cleric
Warpriest
Inquisitor
Paladin
Melee centric
Excluding the commoner faithful, and those that are followers but don't draw their powers from the deity, how would the 4 classes (did I miss any?) serve the deity? Like...
Cleric - Forms the body of the followers, acts as teachers
Warpriest - Like cleric, but more combat focused
Inquisitor - Solo field agents, works behind the scenes
Paladin - Solo leaders, looks to lead through actions
Does this sound right? Please feel free to correct my head cannon. Also feel free to add any prestige classes (like Holy Vindicator) or other classes I missed.
Classes don't come with built-in personalities. Any divine character can do his divine stuff however they feel appropriate. In a lot of cases, which god they follow makes a huge difference. A cleric of Gorum, for example, is not going to act as a teacher, except maybe to teach people to fight. A Warpriest could be a pacifist, fighting only when absolutely necessary. Paladins don't automatically take charge of things.
Don't forget druids, adepts, hunters, and onmyoji.
Depending on how a cleric is built, he can be a supportive caster, a melee juggernaut, a healer, an archer, and so on. Inquisitors are just as varied. The role of a character is chosen by the player. My last cleric was not a teacher, nor a missionary. She was on a quest from her goddess and served as support and healing most of the time. The paladin was not our leader, though he did serve half the time as the party face. He was our front-line tank.
An individual character can serve different deities in different ways, and the Faiths of Purity/Balance/Corruption books and Inner Sea Gods book actually go into major detail about the worship of each god and what classes they favor (some gods favor non-divine classes, like Shelyn likes bards or Gorum enjoys fighters and barbarians).
A rough summary of my take on the flavor of those classes, based on the way the classes are written flavorwise:
Clerics are devout worshippers who have dedicated their lives to service of their god, specifically as a mouthpiece for the deity. Clerics have a wider range of magic due to their dedication, but lack the martial training of the more warrior-like classes. A cleric would likely profess the wisdom and ideology of their deity within the way they speak, but probably wouldn't turn EVERY conversation into a sermon, just the ones that are important. A well-written cleric keeps the will of their deity in mind with every decision, but still makes their own decisions.
Paladins are devout champions who seek to better the world through virtue and valor, and take on the burden of a strict code of conduct in order to be considered worthy of the considerable power that paladins are granted by their gods. Paladins are given the power needed to take matters into their own hands, so they typically seek wrongs in the world and try to make them right. Paladins may be members of a regular church order or an entire paladin order, or may even have taken the mantle solo. A well-written paladin considers the impact of every action he takes, and feels guilt when his failures lead to a loss for all. The paladin asks not for whom the bell tolls, for it tolls for he.
Inquisitors are a bit of the darker side of the divinity spectrum, even for the better deities. Devotees who use actions rather than words, Inquisitors are more versatile agents who seek to solve the church's problems through subterfuge and subtlety, rather than open resolutions or direct intervention like the cleric and paladin. Inquisitors are typically more quiet about their faith, especially among enemies, but will invoke their deity's name when the time is right to pass their Judgment. Inquisitors know that their actions are more pragmatic than ideological, but it is for their deities will, and so it must be done.
As for warpriests, they're just clerics who integrate more training in combat into their regular devotion. It's more ubiquitous than the other divine classes.
Thanks all for the input - given me stuff to think about.
All divine classes have some combat capability since most divine spell lists consist mostly of combat buffs and out of combat utility.