lift without trimming

I know this has been asked probably a million times but Ill ask again. I am an old/new member of these forums (had an 87xj sold it went a couple years without one and recently bought a 94xj cause I like em!).Anyway I need to lift and was wondering what is the minimum lift I need to put 31x 10.50's on without any fender trimming? I currently am running 30X9.50 BFG's on stock rims and it looks like I still have quite a bit of room. If I go with 31's I want to go with 15x8's. I also need to do this without spending a ton of cash (new kid on the way) . I dont do as much wheeling as I used to and this is a daily driver so I dont want it to get to wild (my 87' had 8" of lift and 35's).Are there any good kits for not alot of money or can I piece something together? Any help would be apprieciated! Thanks.
J

Lift won't matter much. If you don't add bumpstops, it's gonna rub.

I will put in bumpstops if needed or run 15x7's with a different offset.

3" lift, stock 15x7s, bumpstop enough to not rub.