Cleric or paladin for a member of a religious military order?

[Rfkannen]

I was just thinking, when you think holy knight you typically think paladin, but would cleric work better?

What im thinking is representing a member of a military orders such as the templars and the hospitaller (but for a d&d god like bahamut or thor))

Now in 5e paladins it specifically points out that paladins are more tied to justice than a gods cause, and that most of them are adventures. While a member of a military order would probably care more about the rules of the church and their order than justice. So to me it seems that with the fluff of 5e, paladins are not really the type to actually be part of a miliarty, while a cleric might.

Now granted you could just ingore that fluff, and if your just looking at the mechanics of the class it might be different. (Im not sure, whats your opinion?)

Would you use different classes for different orders, if so what classes for what orders?

What do you think about this?

tldr; What class would you use to make a hospitaller/templar?

ps. What domain/oath would you pick?