Does it have stock wheels or aftermarket wheels?
Hopefully it has stock wheels. I think those are best.
If it has 15 x 7 stock wheels, put 30 x 9.5 R15 size tires.
If it has 15 x 8 stock wheels, put 31 x 10.5 R15 size tires.
If it has 16 x 7 stock wheels, put 245/75R15 size tires. That's a 31 x 9.5 R15 tire.
All those will fit on a stock TJ with no modifications needed. i.e. - no lift needed, no regearing needed. Good stuff. The 9.5" wide tires will fit perfectly with your stock fender flares too. I'm not sure if 10.5" wide tires fit under stock flares, but if not, get some used TJ Rubicon flares (a little wider) if you can find them, or buy new ones.
9.5" wide tires will be ideal on Winter roads, and OK on mud. On highway a 9.5" wide tire is ideal for gas mileage, acceleration, quick braking, and won't hydroplane on wet highway.
10.5" wide tires will be OK on Winter roads, and ideal on mud. On highway a 10.5" wide tire works OK, but will sometimes hydroplane a little on wet highway when you hit a puddle at high speed.
I live in Western WA State (very wet highways most of year) and lots of mud off road, and some snow and ice in Winter. I prefer 9.5" wide tires because I drive on highway a lot, especially wet highway, and some times snow and ice. I occasionally have to deal with mud off road too. I prefer 9.5" wide tires because highway and Winter road traction are my priorities, and the 9.5 wide are good enough for the moderate mud situations I occasionally encounter.
But for deep dry sand at beach, a 9.5" wide tire sinks to much and struggles, while a 10.5" floats on too of sand and has an easy time driving on sand.
I don't drive on sand much. When I do, I air down the tires and then the 9.5 are adequate on sand. If I drove on sand more often, I'd want 10.5" wide tires.
As far as treads so, Cooper AT3 is (IMO) the best AT and is available in all 3 sizes mentioned. It is excellent on dry and wet highway, good on Winter roads, adequate for moderate mud, and excellent on sand.
One step more aggressive is Duratrac, which is available in 2 of the 3 sizes I mentioned.
It is good on dry and wet highway, good on Winter roads, good for moderate mud, and OK on sand.
P.S. - The only tire tread that excellent on Winter roads is a dedicated Winter tire, but that's not ideal for your other needs.
Hankook makes a Winter tire that can be run year round and makes a good all terrain tire. I run them year round on my Buick car and they do good on highway; great on Winter roads, gravel roads, and sand; and good for mild mud and marginally adequate for moderate mud. I run them on my car because at the time I needed tires, there were no all terrain tires in a size that fit my car. Now there are Cooper AT3 sizes that fit my car. Next time I'll put AT3 on my car. The AT3 rides as soft and quiet as the Hankook snow tire, but the AT3 is tougher and somewhat better for mud.
For my Jeep XJ, I like both Cooper AT3 and Duratrac, but Duratrac not made in my size. AT3 is made in my size. So it's an easy choice for my Jeep: Cooper AT3 in 30 X 9.5 R15.
Warning: I often edit my posts a few times to get them complete or correct errors.