From a purely technical standpoint, the list of must-haves is not that long. A rope, of coursebecause it will be doubled, an 8 to 9 mm rope will be lighter and easier to handle than a 10 to 11 mm one. An example: Bluewater's 8mm/60-meter rope ($160), which would give you plenty of length. And a decent harness; plenty of good ones, but take a look at Black Diamond's tried-and-true Bod ($50) or Petzl's Corax ($75). Both are good, all-purpose harnesses. For a rappel device, avoid figure-of-eight devices as they can twist the rope. Better a "straight-through" model, such as Trango's Jaws ($20) or Black Diamond's ATC (Air Traffic Controller$15). Both also double as belay devices. You'll also want leather gloves, a helmet, sturdy hiking boots, and a variety of slings to serve as rappel anchors. And a knife on a lanyard in case something goes awry and you have to cut yourself out of the system. Also, learn to tie and use some simple prusik-style ascenders, in the event you have to reverse course and go UP the rope.
Anyway, that's what you need. But I've gotta ask: Why rappelling? Is it for caving, or just for some light recreation? Because, of all the climbing-type activities, rappelling is perhaps the most hazardous. When I'm climbing a pitch, my belay partner and various anchors create a redundant safety systemone part of that can fail without the whole thing failing. But in rappelling, you're hanging on a system that will fail completely if any one part
of it fails. For that reason, many, many climbers I know thoroughly dislike rappelling, and view it more as a necessary evil than some great, fun thing to do.
In any event, don't just go to some cliff, toss down a rope, and have at it. Enroll in a climbing course so you learn the up as well as the down, and learn how to do both safely.