Most stock rims are 15x7 but I have seen some 15x8.
31" tires should fit fine without any real rubbing issues (might rub a little at full lock when steering). 235/75/15 tires will fit with no rubbing at all (but they work out to a 30x9.50x15).
A big possible limiting factor will likely be your gear ratio. There should be a two digit code on the door sticker for the axle, let us know what that is or you can look it up on the tech pages (there's also a metric to US tire size calculator on there).
I've seen people run 12.5" wide tires on 15x7 rims, but I wouldn't advocate it - it gets hard wrestling some of those wide tires on that narrow of a rim sometimes (I put some bias ply 33x12.5x15 tires on 15x8 rims and it was a real bear even with a good tire machine).
As far as tire selection, what are you going to be using the truck for? A lot of street driving? I'd pick a good aggressive pattern, there are plenty out there to pick from. When I pick tires I look for the most aggressive AT tread pattern I can find that fits my budget. I have very little brand loyalty (probably partly because the last two brands I liked I can no longer get). If you're going to be in the mud a lot or offroad a lot, you'll probably want to look at MT tires.
If it's all playing around on the road and you live somewhere that you don't have to worry about snow, a tighter tread pattern like the BFG AT would likely last the longest. But I hate them for around here - I don't like their performance in snow and they totally suck in the mud around here (and yes, I realize that most AT tires suck in mud).