When you look at the pre-packaged sets, the heads they come with are not quite good heads. They'll get you started, but they'll be less durable and will not sound as good to begin with. Something like Remo Ambassadors or Evans G1 heads would be a good place to start. A Remo Powerstroke 3 or Evans EQ3 on the bass drum is also a good bass drum head. I would recommend putting good heads top and bottom on any kit you decide to buy - it's like putting new guitar strings on a guitar. You'll be doing it all the time if you want to have a consistently good sound.
Zildjian makes an A. Zildjian pre-pack, which I think includes 14" New Beat hi hats, a 20" medium ride, and a 16" thin crash, which shouldn't run you more than $600. If you get something like this, I guarantee you will not have to buy better cymbals ever. You could use these for your whole career and never have to upgrade, and when you think about it, you play more cymbals than anything else. This will leave you somewhere around $400 to find the drums, and better heads.
I just did a review on the Sonor Bop kit, which is $400, but you still need heads. Mapex (with a nod to Sticks) also has some intermediate kits, but I don't think they'll be this cheap. You'd also still need hardware. I think you need more money. Let's say 2K should be your limit, then.
You can do whatever you want, but trust the theory that you want good cymbals FIRST. I can take any drumset and make it sound good, you can learn how to do that too. But bad cymbals will just sound bad, so you might as well get it over with and get the best you can. Usually, people asking for advice here will usually spend all their money on the drums and then buy crappy cymbals, only having to upgrade a couple of years later, spending even more money to fix a mistake, because they won't believe us to begin with. I think it's like some kind of rite of passage.
Get a copy of Modern Drummer magazine and see what's advertised and start looking at what guys are playing. There's so much stuff out there that it's easy to get overwhelmed. Having us tell you what you need will only confuse you more.