To run 35's that are 12.5 wide, you will want backspacing somewhere around 4.5". Stock rims on the JK are at 6".
A budget boost will make room for 35's without any issues...but if you're not going to offroad it, you can probably stuff 35's in there just by trimming the pinch seam on the front side of the rear wheel wells. As far as which BB kit to get, I'd probably buy the Currie leveling kit - but to be honest that's just based on the quality of their parts in general.