I believe you have a 3500 lb tow rating. If that's correct, you want something under 20' overall length, and about 2500 to maybe 2700 lb dry weight. It's very easy to have such a trailer weigh nearly 3500 lb in real life, once you add LP, battery, water, and gear. Also it becomes difficult to keep hitch weight under 350 lb, so you want something with a dry hitch of 250 or less.
The Wranglers are not noted for great handling because their center of gravity is a rather high (or at least they used to be that way) and the wheelbase isn't very long. So they are not the greatest tow vehicles. But they can work. Really, if I had a Wrangler, I'd be looking at small popups. They have plenty of bed space.
