Climbing - Equipment
In fact, if you are climbing with a guide as mentioned above, he will usually provide the necessary equipment. If you are planning to climb on your own, even part-time, then yes, you should bring what you will need. It is fairly easy to arrange for somebody to drive you out to a climbing site and meet you again at whatever time you fix (even though this isn't free!)
No climbing equipment at all can be hired in Wadi Rum. If anything is offered to you either for hire or for sale, you should be very careful about the quality of whatever is proposed, in particular the ropes.
Other equipment : if you are expecting to camp, then a minimum of cooking and camping equipment is necessary, and this includes a good sleeping bag. The main season for climbing in Wadi Rum stretches from October to April, so be prepared for cold nights. (Snow is not unknown in January and February !) You may well be happy in a tee shirt during the day, especially if you come from Northern Europe or its equivalent on another continent, but the temperature drops rapidly as the sun goes down. It is probably easier to hire a tent when you get there, but as said above, you cannot count on finding cooking equipment in Rum Village. If you are with a guide, then again all camping equipment will almost certainly come with the package.