Most of the routes in Rum are free, or can be climbed free, you do not need to be an aid climber to climb in Rum, nor do you don't need aid gear, unless you specifically want to do one of the serious routes like The Red Sea or The Towering Inferno.
For most of the free routes in Wadi Rum you will need two 50m+ (or more) double ropes, a full set of nuts, full set of cams and a pile of tape and cord for threads. This is appart from the ussual 14 or so quickdraws, harness, daisy chain, shoes etc. Climbing in Rum can be very hard on your ropes, and you would be better off having a spare set, in case you destroy, damage or wear out a rope or two.
In addition to the above rack you will need a full set of varying types of pitons, hammer, hooks, daisies, etriers and perhaps a single rope, or two for leading, fixing and jumaring etc. Except for perhaps one or two routes, or maybe new routes you should not need hammocks or portaledges. There are large enough ledges for bivouacs on most of the long routes, take a haul bag and a hauling pulley for these routes, unless you move fast enough to complete them in a day.