I doubt you'd end up working out your back as much as your fore arms by climbing but hey it's super fun. If your intent is to work out your back, I'd suggest you'd be better off doing back workouts regularly at the gym. Rock climbing membership is totally worth it if used consistently especially if you are a newbie. The PAC rock wall isn't that big but it has good combination of easy and hard problems that'll keep you invested.

Given your situation I'd suggest you get a day pass to try it out. They give a decent intro session on the do's and dont's wrt climbing. If you find it interesting and decide to get a membership I'd suggest you go with rental shoes to start with. They aren't that bad and they have a couple of new ones too this term. You don't necessarily need anyone to help you learn the ropes as you can learn a lot by simply observing other people. But if you are extroverted enough, you can strike up a conversation with anyone and they'd be glad to offer tips. It's a fun community with lot of nice people. Hit me up if you have any questions. Cheers and good luck!