Order of warrior priests is probably more fitting. Let me think some more on the nature of that order, as I have a couple of ideas I need to sort through.

I'm leaning towards a crusader type, but more like an agent of the church dispatched in special or particularly important circumstances. Or perhaps more of a spiritual strongarm type, one who belongs to an order that is often used to maintain order and the integrity of the church at any cost. Depending on the set up, this could lead to being wellknown and disliked, or just unknown. haha Either way, the order is more martial than your run-of-the-mill cleric.
As far as the Greek pantheon... I would say Zeus or Athena is most likely. Zeus in that he was considered the guardian of kings and later of the democratic state, and of coure an able warrior as chief of the pantheon. Athena in that she also possessed great martial prowess as well as being the same type of "level headed" that I mentioned in my previous post. So if I go with the strongarm type it'll be more geared towards Zeus, and then Athena otherwise.
Those are my preliminary thoughts anyway.