The Computer: This will be your work horse, so choose wisely.
Modern computers are more than capable of recording music by simply adding an audio interface. Although with the improvements being made to USB based studio gear it has become possible to record high quality takes without needing to invest in an analog hardware interface. Make sure to look around before choosing which computer you need because the type of gear you decide to use with it will make a big difference.
Recording Software / Digital Audio Workspace: The backbone of your studio.
There are numerous options available when it comes to buying recording programs and plugins. It's important to choose software that fits your requirements. Some of the largest are ProTools and Adobe Audition, but feel free to look around when choosing what will work best for you.
Hardware Controllers: For those of us with a hands on mentality.
A hardware controller in its most basic form is a MIDI or USB controller which sends messages to your computer with a traditional analog feel. They come with all sorts of functionality, from Turntables to Keyboards and other studio gear, so feel free to look for the best equipment that does what you need it to do. Quality digital based hardware is in most cases on the same footing as their analog competition, so shop around to get the most bang for your buck.
Microphones: Because you need to record, right?
The mic is such an important part of the overall studio that you can not afford to go be stingy when selecting your mic of choice. In most cases, you will be more than happy with the results you will get from a top end USB microphone. A good price range to expect for a quality piece of hardware is in the $ 75- $ 150 area depending which brand you choose.
Headphones & Monitors: For recording and mixing.
The system you choose to mix your music on makes a huge difference in the final project, so again, get the best you can afford. A good sound system can massively improve the quality of your mixes, as it will more accurately capture what your recording. When choosing the speakers that you plan on using for mixing make sure you get speakers that are sonically neutral, or in terms terms, they show no preference to highs, mids, or lows, and have a well rounded sound. There are several good brands of recording headphones to choose from, the biggest things to look for are a long enough cord to reach from the audio equipment to the booth and a good frequency response.
Acoustics: The most important factor in a clean recording.
Its easy to overlook acoustics when laying out a home studio. Honestly though, this is one of the largest elements in how clean your final project will sound. It's easy to get lost in where you want the equipment to go than the acoustic physics behind room reflections. If your room has a lot of reflections, which is easy to identify by a light echo or reverb when you talk, it is easily rated by acoustic panels. You can search Google for the most effective ways to sonically treat your recording area.