If you plan to stay with 31x10.50 tires and never go any bigger, go for a 15x7 wheel. The wheel will need to have a 5x4.5" bolt pattern and have backspacing between 3.75" and 5.25" of backspacing. The more backspacing, the further into the wheel well the wheel will be positioned. For example, a wheel with 4.75" of backspacing will be positioned 1" further inside of the wheel well than one with 3.75" of backspacing will.
For a 31x10.50 tire, I'd choose a 15x7 wheel with 4.5" of backspacing and that 5x4.5" bolt pattern. That's for if you will never go with a bigger tire.
If you think you may eventually go with 32x11.50, 33x12.50, or even 35x12.50 tires, go with a 15x8 wheel with everything else remaining the same.