A computer's main function in home recording is storage. A computer that is about a year old is affordable and will support your recording needs. Look into buying a tower and monitor if you don't already have one. Laptops work, but towers provide more space and don't heat up like laptops during heavy use. Budget a minimum of around $600.
A multitrack recorder allows you to record tracks before uploading them to your computer. This device is handy if you plan to record multiple tracks at the same time. Most multitrack recorders have a memory card where the data is stored, so be sure the memory card is compatible with your computer before purchasing one. If the memory card isn't compatible, talk to your electronics store representative about a USB device you might need. Multitrack recorders usually start around $100.
A good pair of speakers and headphones allow you to hear your recordings in detail. Don't spend more than $200 combined unless you want to. Speakers with a remote work great because you can be anywhere in the studio and adjust the volume when necessary. Logitech speakers are affordable and offer great sound. For headphones, you'll want to look for ones that cover your ears. Skullcandy has a line of these that come in a variety of styles.
Recording studio software is beneficial for mixing and editing. A variety of software is available depending on what style of music you're recording. Samplitude Music Studio is ideal for any type of music recording, whereas FL Studio is geared toward MIDI recording. Shop around and research which software will work best for you. Reliable recording software starts around $80.