>>940255You're going to want to familiarize yourself with rappelling and some basic anchor building.
Look for anchor building techniques that involve using a tree for an anchor and translate that to whatever similar urban feature you can use instead.
Also for getting back up you're going to want to use an ascender most likely. Unless you have a partner who already knows how to climb and can belay you from above while you climb up unaided.
To answer your question though, you'll want a rope, harness, belay device, a locking biner or two and an ascender. If all you're doing is rapping and using a jumar to go back up the rope you can buy a static line. I'm only familiar with dynamic ropes used in actual climbing, but I believe a rope intended for canyoning is going to be what you want. Make sure the rope you buy is the appropriate diameter for both your belay device and ascender. If you can't afford an ascender look up prussiking.
