Here's the few things you need to start climbing. This is assuming you have some good friends that have the major equipment for outdoor stuff (ropes, hooks, etc.)
Shoes at the gym really suck. Really. The millions of people who have worn these shoes before you took off any and all traction th shoes may have had. For a beginner, the La Sportivas are my favorite. They have some style, traction, and are at a reasonable price. I liked the laces on the shoes because they didn't make me feel like a Velcro child. If you ask for the opinion of the clerk at your local outdoor shop, he or she is going to tell you to get shoes that "hurt". Ignore them & get these shoes. You're a beginner and don't need to bogged down with that level of pain... yet. Also, you shouldn't listen to people who say you SHOULD be in pain.
You can use the climbing gym's harness, but what you're giving up is nice under-butt padding. Not a HUGE deal, but makes climbing a bit more comfortable. This is my favorite harness.
Pants that cover your knees
I've banged up my knees so many times through climbing. It helps to have some cloth as cushion there. Trust me. Me & my knee bruises.
Climbing makes you thirsty. Like REALLY thirsty. Maybe it's all the chalk in the air but yeah.
You can get any old belay loop, but the Gregory- OMG the Gregory. It is beautiful and easy to use. When you're a petite girl, trying to belay your larger partner, you sometimes let them drop a bit... and they get mad at you. The Gregory holds that person STILL. Again, not necessary, but it is awesome.
Any other must haves for rock climbing that I'm missing?