Exiling Creatures: When is the card face up and when face down?
If the ability says to exile the card face down, you exile it face down. Otherwise, you exile it face up. Banisher Priest doesn't say to exile the creature face down, so you exile it face up. Rule 406.3 says


  Exiled cards are, by default, kept face up and may be examined by any player at any time. Cards "exiled face down" can't be examined by any player except when instructions allow it. However, once a player is allowed to look at a card exiled face down, that player may continue to look at that card as long as it remains exiled, even if the instruction allowing the player to do so no longer applies. A card exiled face down has no characteristics, but the spell or ability that exiled it may allow it to be played from exile. Unless that card is being cast face down (see rule 707.4), the card is turned face up just before the player announces that he or she is playing the card (see rule 601.2).


One thing to keep in mind is that the point of exiling a card face down is to keep players from knowing what it is. It wouldn't make sense to exile a card face down if everyone already knows what it is. The only abilities that say to exile face down are abilities that exile from hidden zones: the hand and the library.