I recently started getting into rock climbing (top rope climbing), only indoor right now. I’d done it a few years back but never really got into it, but now I’m jumping in with both feet, so to speak.
You can rent gear, but you really will want your own gear. It lets you get more familiar with everything, something very important when your hanging 30′ off the ground and it will save you money if you plan on climbing a lot. You should definitely rent, if it’s an option first to see what you like, but eventually, it’s definitely worth buying, especially if you are planning on getting out of the gym eventually.
I ended up just buying some stuff, and did a TON of research, and I’m quite happy with what I ended up getting, but I did buy a lot of extra stuff in trying to figure out what I needed/wanted. I’m also a gadget guy, so the extra stuff (mostly carabiners) I’ve found uses for so it wasn’t too bad. But after a couple weeks of having and using the basics, this is what I could have ended up with and been completely happy.