Boxes are the only place where you will get gold and items. Only Thieves, Ninjas, and Samurai have a realistic chance of detecting and disarming traps (Thieves are best). Your priests do have a spell which will disarm traps, but you have a limited number of these. On the first few levels, the traps do not pose that great a danger, but on the lower levels, they can be deadly (particularly the exploding box).
I would also like to say that if you are putting together your first party, don't worry too much about the composition. This is a generational game, and the party you end up with is likely to be very different than the party you start out with. However, it is actually pretty easy to level new characters after you get the hang of the game. In fact, I find that bringing up new characters with different class/race combination is actually quite enjoyable (but that may just be me).