DeJaBu,
With the budget you're talking about you would come no where near close to a killer home recording studio. $3000 is a good start though. I don't know what Eminem has in his home studio or how that even matters.
Do you want to produce and/or record vocals? This matters greatly because you need specific equipment for both. If you're talking strictly production this is where you'll want to start:
1. Decide if you want to go with software or hardware (or a combination of both).
a. If you decide software you'll need a relatively fast PC and a good audio interface as well as MIDI ports. You'll also need a bunch of software; sequencing, sampling, virtual instruments, etc. You'll probably also need some sort of keyboard controller. ($750 - $1500 to start unless you have a PC that's ready to go)
b. If you decide hardware you'll probably want to start with an all-in-one unit like a groove box or a Triton or Motif. From there you can add additional sound modules, samplers, keyboards and drum machines. Be prepared to purchase a mixer and outboard gear like compressors, EQs and/or effect processors. ($750 - $1500 to start)
For recording vocals you'll need to:
1. Again decide if you want to go with hardware or software (or a combination of both).
a. If you decide software you'll need a fast PC with good audio interface (MIDI ports would be handy here as well). You'll need multitrack recording software capable of handling plug ins. You'll probably also want a wave editor. (shared with production costs).
b. If you decide hardware you can go with one of the Roland all-in-one recorders. Or you can choose a HDR like the Mackie units, but with that you'll also need a capable mixer. (starting at about $1000)
2. Of course, either way you'll need a nice condenser mic (Shure/ AKG)and most likely some sort of channel pre-amp. (starting at about $400).
There are other variables as well depending on what type of system you choose, this is just a general idea of what you'd be looking at. Either way I would say $3000 will get you started, but for a killer home studio (which after $8000 I'm still chasing) be prepared to spend a considerable amount more. Don't forget about the time you'll have to spend learning these devices.
Good luck.
Stray