Well, the most important thing if you are considering an acoustic set is the noise... Believe me no one wants to hear drums even if you're really good, so make sure your neighbors/parents whoever doesn't care first.
If noise is an issue get an electronic set. The Alesis DM5 electronic kit is in your budget:
http://drums-percussion.musiciansfriend.com/product/Alesis-DM5-Pro-Electronic-Drum-Set?sku=490095Or this Simmons, but I dono if I would recommend it personally. (I have a DM5 Module I use for triggering double bass on an acoustic set).
http://drums-percussion.musiciansfriend.com/product/Simmons-SD5K-Electronic-Drum-Set-?sku=443369If you happen to be one of the lucky ones who can make noise any time you want... by ALL means go acoustic, there are some beautiful kits out there under $1000. My personal favs are Sonor Force 3007 series, Pacific Platinum Lacquer Series and Gretsch Catalina Maple.
http://drums-percussion.musiciansfriend.com/product/Sonor-Force-3007-Studio-1-Shell-Pack?sku=490526http://drums-percussion.musiciansfriend.com/product/Gretsch-Drums-Catalina-Maple-Fusion-Drum-Shell-Pack-with-Free-16-Floor-Tom?sku=483246http://drums-percussion.musiciansfriend.com/product/PDP-FS-7Piece-Double-Bass-Shell-Pack?sku=583364Maple is hands down the best tone wood, DO NOT buy anything basswood and try to stay away from poplar as well. Birch can be nice, but for me Maple just has that perfect blend of warmth and resonance... beautiful sounding toms
If you end up having to spend a little more to get a maple kit - DO IT. You will not regret it later. Please do not buy a "Pulse" or other beginner type set, yeah you get a lot of drums for the money but they suck, believe me. I have a cheap Pacific EZ series kit, but after hearing a few maple kits at Guitar Center I was sold... I just don't have anywhere to play as often as I would like so it doesnt make sense for me to spend $2000 on a nicer drum set just yet... so I make do.