if you want to def stay at a 31" tall tire then i would stay at the standard 31x10.50. Tread and tire quality is what will make the most difference in my opinion. I ran with a Pepboy tire: Dakota MT. in my opinion, those were a wonderful tire. Not expensive, lasted a good while and did real well off road. My buddy who i 4x4 with has 31" BFG All Terrains on his 4.0l TJ and ive had to pull him out of mud multiple times while i CRAWLED right through with no problem. those tires had some great grip. Also, if you do end up wanting to go bigger but want to keep it narrower than the standard 33x12.50, Dakota also makes the equivalent of a 33x11.50 MT. At the time i was shopping for an upgrade, that was the size i wanted but they were on back order so i ended up going with the Toyos.