If it's a stock tj rubicon, they are capable jeeps, they have good flex too. If you're not ready to lift/modify the suspension properly and replace rims. Id look for a stock size tire of 245/75R16, if you want to go up one size to 265/75r16 I think you could get away with it, maybe minor rubbing when the sway bar is disconnected and off road.
Tire options are plentiful these days, which is good. Most name brand off road tires these offer excellent performance off road and on the street.
Goodyear mt/r Kevlar
Mickey Thompson MTZ, baja claw, atz p3, deegan 38
Toyo MT, AT2 extreme
Cooper stt
Nitto trail grappler
These are tires I've tried or I've seen them work very well in all conditions.
Also when it comes to tires you'll get many opinions... Just warning