I am investigating tow options as well. My quandary is choosing between an F150 Supercab 4x4 or a GMC Sierra, or going big with a 3/4 ton like an F250. I would prefer the smaller truck because it will be a daily driver.
Generally speaking, the tow rig needs to be able to flat tow 5,000# easily, preferably 6,000# since some armored rigs can exceed 5,000# when fully loaded with fuel and gear, especially LJ's. For towing with a trailer a 7,500# tow capacity is the absolute minimum I would consider for a tow rig.
Another thing to bear in mind is that most states now requires a flat towed vehicle to be equipped with auxiliary brakes such as a Brake Buddy, etc., which can be expensive and narrow the gap between the cost of flat towing and the cost of a car hauler trailer. The days of being able to get by with a cheap tow bar, a couple of chains and some magnetic lights are over.
My initial advice is that before you go much further you have your jeep weighed both loaded and unloaded so you know what you are working with. I think many people underestimate the weight of their jeeps. My LJ Rubicon with hard top has a published curb weight of 4,012#. However, as modified with driver and full tank of gas but no gear, it weighs just over 4,800#. Fully loaded for a week long trip with gas, gear, spares, food, ice and extra fuel and water it weighs just over 5,300#. A friend's LJ with fully armored body weighs 5,800# with his hardtop installed.