Purchase a desktop computer or laptop with a good music production program. There are a number of simple-to-use, inexpensive programs available, such as Apple's "GarageBand" or "Audacity" for Windows. Your computer should have ports for audio cables and instruments.
Purchase an external microphone and microphone stand. Internal microphones on most computers are insufficient for recording high-quality tracks. Purchase several different brands to see which works best for you.
Purchase a strong set of monitor headphones. They should offer deep bass and a wide dynamic range to pick up all the nuances in your recordings. Headphones provide producers with better performance than external speakers.
Set up a self-contained area such as a closet or small bedroom to use for the studio. Soundproof the room to eliminate outside noises that could negatively effect the quality of your recordings. Attach Styrofoam insulation to all walls and ceilings, then add a layer comprised of the bottom halves of egg cartons above that.
Furnish the studio with a couch and enough chairs accommodate several artists at one time. Make sure it's comfortable, but ergonomic. Add posters and artwork of famous rap artists to create a "rap" vibe.