I think the bolt pattern is 5 x 4.5 IIRC and I have 4" backspacing on 8" wide wheels, gives it a little wider stance than stock but doesnt stick out horribly on the sides plus the big sidewall on my tires bulge out to the sides too. No rub.
Not sure on what size diameter rims your going with and what backspacing to go with Ill leave that to others that know more about big wheels on the Jeeps.
As far as tire size, my 31x10.5s went on a couple weeks before the lift and at stock suspension height the tires rubbed on the plastic wheel well lining, had to cut out little pieces of them so it wouldnt rub while making tight turns.
I would say 31s will rub a little at stock height. Probably trim something like I did or get a 2" budget boost which is super cheap or something and you will be good to go. Probably could run bigger wheels that way too if thats what your looking for.
I know yours is a Cherokee and mine is a Grand Cherokee but they are pretty similar. Maybe some of this will help. Im sure other will chime in.