All climbers eventually need to develop their own climbing rack. As a beginner you generally hire or borrow the gear you need, but later on you will definitely need to buy and maintain your own climbing equipment.
What you will need depends very much on the type of climbing you do. If all you ever climb are sports routes then a set of quickdraws should suffice. For everything else you will need a little more equipment in your rack.
For traditional rock climbing you will almost certainly require a couple of slings, a set of nuts, some rockcentrics, a few quickdraws, etc. This still should be pretty low cost and will get you so far.
Make sure once you have bought your rack that you clearly name your equipment. While people stealing equipment out on the crag is rare, it is more likely that your gear will become mixed up with someone elses, or you will just plain lose it or leave it behind en route. You can use coloured tape to mark your territory, just be sure that you use a different colour tape to the ones your friends or climbing companions use.