Welcome to the forum Travis. Maybe we can help.
Yes, a 31x10.50R15 will fit your TJ on the stock wheels. Before you make your purchase check out our selection. We guarantee the lowest delivered price and Shipping is FREE. If you purchase any 5 tires for your jeep give us a call and mention this website. We give WF members $50.00 off their total instantly. Also, if you purchase a wheel and tire package we'll mount and balance them for free before we ship them to you so they arrive at your door bolt on ready.
As for wheels, If you plan on installing a lift at some point and you think you'll want to upgrade your tires to a larger size in the future as well I'd recommend looking for a wheel that is 15x8 or wider. I'd also recommend spending a little more and picking up an inexpensive aluminum wheel. Aluminum wheels are about 20% lighter in weight than steel wheels and they're a lot easier on your suspension parts, and drivetrain over the long run, not to mention saving you money at the pump.
Here's a link to some of the 15" wheels we offer for your TJ, I'd recommend looking at the MB Razor or Level 8 Tacker.
15" TJ wheels: Wheel Products - Discount Tire Direct