The home studio starts with your computer. If your studio will revolve around ProTools LE, Digidesign recommends that your Total System RAM operate from 4GB. Your computer should have a bare minimum of 15GB of free space on your startup drive to avoid latency issues. Logic is another popular music production suite that requires a Mac computer with an Intel Core Processor. With Logic, you can get by with at least 2GB of RAM and about 10GB of free space on your startup drive.
An interface will help you get sound in and out of the computer. Typically, interfaces are offered as external devices that connect through a USB port to your computer. Do not rely on the built-in audio input on your computer as it is rarely of sufficient quality for reliable use. Most interfaces, such as those provided by M-Audio, are bundled with an audio editing software. The industry standard interface for home studio recording is the M-Box. This will get you an interface that meets Core Audio standards plus ProTools LE mixing software. If you decide to go with Logic audio editing software, any interface that meets ASIO or Core Audio standards will work to input sound into your computer.
Now that you are ready to record live sound, you are going to need excellent monitors to properly mix and edit your sessions. Headphones are efficient for checking performance idiosyncrasies and fine details, but monitors are crucial to perfecting the mix of the song in its entirety. Typical stereo speakers will not provide the full range of sound required to properly edit the mix. In a home studio, you will want "near-field monitors." The term "near-field" refers to the placement of small to medium-sized speakers to each side of your working environment. A set of two near-field monitors will be sufficient for a professional mix down. KRK, Yamaha, and Genelec manufacture a wide variety of affordable near-field monitors.
For most home studio projects, you will need to purchase a quality condenser mic. Directional microphones, commonly used in live scenarios, lack the ability to capture the full range of frequency from an instrument or voice. There are many decent condenser mics on the market for surprisingly affordable prices. When shopping for a condenser mic make sure it has the ability to switch between directional and omni-directional. This is important to the types of instruments you are recording. As a general rule of thumb, when you are recording a voice the mic should be set to pick up frequencies of the entire room and with an instrument it should be set to pick up only the frequencies of space surrounding the instrument.