First, try to go the first time with someone experienced with the area. You can always hook up with someone from one of the local Moab 4x4 clubs. It is a very large area with some serious obstacles, you should not try too much alone. If you come out during our annual Cruise Moab event, typically during the first week of May, we'll make sure you have a good time and are safe. Be sure you have a CB radio, HAM is even better, and tell someone where you are going and when to expect you back.
There are many trails you can run safely in a bone stock FJ40. Spend as much money as possible focusing on getting the rig in tip top running condition first with a focus on reliability. This is not the time to jury rig stuff or cut corners.
Taller tires give you more ground clearance, but then you need lower gears. The more gearing you have, to allow you to crawl in Moab, the better. If your rig already has 4.10's in it you are OK for starters. If it has 3.73's then better gears are a good idea. Try starting with nothing bigger than 33" tires to start with. That way you get more ground clearance without excessive body lift. If you can swing it, put an ARB locker in the rear, the next best choice is a detroit locker then a Lock-rite in that order. A roll bar is mandatory and a roll cage is strongly advised.
Randy Rosetta KDØKWX TLCA #19351 69 FJ40 "Meanie" & 1970 Boss 302 Mustang