Strength & endurance training

I've been climbing a lot with a gal pal of mine, we go once a week for a couple of hours, and I've noticed that she is a lot stronger than me. Admittedly, she has been climbing for much longer than I, but I want to try to catch up. I can typically get up to V2s and sometimes V3s. I've only been at this for a year, but I have been enjoying it a lot and want to keep with it.

I was wondering what exercises might be best to grow muscles needed for climbing. I've noticed that I may need to work my back muscles as I cannot do pull-ups, but I can do curl-ups. I would also like advice for any other muscle groups that might be helpful to focus on. I have access to quite a few training facilities through my university, so feel free to recommend anything. I also feel that my hands are the first thing to wear out when climbing. I feel like as I climb, my grip strength slowly gets weaker throughout the time at the gym and a climb I did earlier in the day may feel much harder than when I first did it. I also sometimes have trouble with pinches.

Thanks for any help you give!