I kind of jumped right into climbing when I first started. I had only gone climbing a couple of times indoors when I decided that I wanted my own gear. I also knew that I wanted to go climbing outdoors and I figured I should have some of the basics.
When you first start climbing, the key is to buy good shoes. If your feet are in pain, you’re not going to want to keep climbing. Forget the really intense shoes with a ton of arch, get something that you can tolerate wearing when you’re climbing. I personally found the La Sportiva Nago to be a great shoe.
Besides the shoes, you don’t need to spend much money at all. The easiest way is to just buy a starter package which will have the harness, belay device, a locking carabiner, chalk, and chalk bag. That’s more than enough to climb indoors and is plenty if you’re climbing with a guide outdoors since they’ll have a helmet you can borrow.