Anything over 2" suspension lift and 31s is an expensive can of worms on a TJ. IMO if you want to vave fun on a budget (and there's lots to be had) and keep it a daily driver;
Stick with your 31" tyres
Fit a 2" budget boost (spacers so you keep the stock ride quality and cheap as chips)
Fit longer gas shocks.
Fit front swaybar disconnects to aid articulation
If you still want a taller wider look get a set of 8" rims with 3.75" backspacing and fit a 1" body lift. (the rims will also address the rubbing without losing the nice tight turning circle a Wrangler has without messing with the steering stops. You might get away with the stock fender flares like this, but if you fit wide ones the wheels should be wide enough to fill them and look good.
Following from Peters £-ometer here's a TJ tyre-ometer
31"- no lift required but minor clearence problems without 2" lift offroad, slight loss in performance but tolerable.
33" - requires lift of at least 3", preferably to suspension, this leads to the need for SYE mod to transfer case. 8" rims and extended fender flares required. Starting to get noticably more thirsty, performance severely impaired without regearing, brakes start to struggle a little, steering system now at the limit of what it can do without modification. Becoming a pain in the a$$ to use without all required mods done properly.
35" - requires big lift, reworked steering plus all of the above, regear essential or will be pretty unusable on the street, strength of axles and other driveline components very questionable at this level, brakes puny and fuel consumption terrible. With a lot of expensive work, can be made into a reliable daily driver, but even then will be a very different ani,al to stock.
Also, be warned. Stay out of deep water unless you have extended the breathers for axles, transfer case and gearbox. If you have the old 3 speed auto tranny it has to be removed as the original breather is a hole behind the torque converter and has to be plugged and a new one drilled in the top of the housing. If you get water inside it'll be toast.
