31x10.50R15 is a good tire choice that would work well for you. Add the H&R springs, a BL, then enjoy the Jeep. FWIW, 4WheelParts has a buy 3 get one free going on now. I just picked up a set of MT ATZ P3s for my 31" tire build.
I'm not at home right now but I'll check after vacation. They were part of the hardtop package that was put on just before I bought the jeep. I've since gone to full doors and only use these in the summer with and without the uppers.