So when it comes to JK’s the General rule is a 2.5” lift will happily clear 35” (315/70R17) tires on a lower backspace rim.
A 285/70R17 (33x11.50R17) fits with no lift with a low backspace rim. And 285/75R17 (34x11.50R17) is a good half way point that needs only a 1.5”-2” lift to fit. I like the last option because it gives you the bigger tire but not so big it stresses your steering, suspension, drivetrain and brakes. Also, any lift higher than 2.5” needs exhaust mods to clear the front driveshaft. And your driveshafts won’t like the steeper angles either.
A basic lift with good shock absorbers and adjustable track bars will make you like your jeep a lot more than you already do.
Plenty of tire options to choose from. But if it’s a daily driver find a good all terrain winter rated tire.