Decide whether you want your drums and cymbals to have individual stands or if you want everything to be contained on a drum rack, which is basically a scaffolding for the individual pieces. If you don't plan on moving the drum set around a lot, individual stands are fine. If you play a lot of gigs, the drum rack's use of clamps gives you the ability to reassemble your kit the same way every time. It will also save you a lot of space because everything is mounted to one sturdy stand.
Buy drum shells. While a snare drum and bass drum are a must, the number of tom-toms you can get is completely dependent on your playing style--and maybe your wallet. You should get at least two. A high- and low-pitched tom work well, maybe a 10-inch mounted tom and a 16-inch floor tom, but after that it's up to you. If you like big sweeping tom fills, get as many as you can afford. If you want to keep it simple, stick with two--Dave Grohl rocks two toms.
Buy drum heads. Here's where your own style comes into play more then anything. Drum heads come in a variety of styles and can be tuned any way you want--unlike stringed instruments, there's no standard tuning for drums. If you like a brighter sound to your drums, go with clear drum heads. If you like them to sound warm, go with coated. Tune the drums to whatever sounds "right" to you; just remember, tuning is an art that must be mastered. Get someone who knows what he's doing to help you put drum heads on for the first time.
Buy cymbals. Here again, the amount of cymbals and the sounds you want from them are all dependent on preference. You'll need high-hats, but after that it's up to you. You will find a ride cymbal to the drummer's far right side and a crash cymbal just to the right of the high-hat on most standard kits. But if you want to make a lot of noise--like bands from the 1980s did--there's a seemingly endless amount of cymbals you can get.
Put it all together. If you chose the individual stands, you'll need a snare stand, a high-hat stand, one stand for each cymbal and tom arms that will attach your mounted toms to the top of the bass drum--floor toms will come with legs. If you chose the rack, you'll still need a high-hat and snare stand. But for everything else you'll need pipe clamps--often included with the purchase of a rack--that will hold the tom-tom mounts and boom arms for the cymbals.