I would recommend a decent sound card, mixer and monitors.
For mixers, you can pick up a cheap 8-track for a few hundred bucks, maybe even less. I used to use an Art 8-track mixer. It's nothing fancy, but for the purpose of patching together mics into a single L+R main output that your sound card can take, it does the job. The pre-amps aren't great but passable for sure. Also it's handy if you ever wanna use it for stuff like ripping old vinyls or tapes to your computer, or basically any application where you'd like a digital copy.
For sound cards, I would check out some of M-Audio's cheaper cards, they make some good stuff. The goal with sound cards is to get a response time that is as close to 0ms as possible. What this means is that, while you are recording, you want the lag between when you actually play to when your computer records the digital waveform to be as little as possible. I have an M-Audio Delta 1010 which is a dedicated rack-mounted sound card. It advertises a 0ms lag time, but Cubase reports it as 2ms. The cheaper M-Audio stuff will still have very good response times. For reference, most consumer-level sound cards have response times of up to 1 second, which is absolutely catastrophic for recording music. In some songs, 1 second of music can equate to several bars.
As for monitors, I also have some cheapy M-Audio ones. Looking to upgrade soon, but right now I have the LX4 set. They were a few hundred bucks. They aren't too bad. I would think of them as a spruced up pair of stereo speakers. I would suggest going to the local audio shop and asking to hear some monitors in action. My local Long & McQuade has a "monitor wall" with various pairs of monitors hooked up and ready to listen to. That way you can just come in and say "my price point is $xxx, show me what you have" and they will show some options for you.
I think you should be able to nail down some decent gear for $1000. I reckon the mixer should be cheapest.
Also, a good computer is necessary too. Keep your HDDs defragged on the regular, and a fast CPU with as much RAM as you can throw at it is good. Also, schedule your CPU to prioritize background tasks (IE: incoming audio streams from the sound card), rather than programs.