Check the minimum system requirements for whatever audio recording program you plan on using. While there are many other things to consider, you need to know what the manufacturers of programs like Pro Tools, Logic or Cakewalk recommend before purchasing a computer, even though you will want a computer of better quality than recommended by each company. This information is generally available on the audio program manufacturer's website.
Purchase a computer with at least one Firewire port. All high-end audio interfaces and programs run using a 1394 Firewire connection. Firewire is much faster than USB, making it more reliable for serious recording applications.
Make sure the computer you purchase has at least 2GB RAM for basic operation. If you are going to be doing very large sessions that have many tracks, or if you are going to be using an HD program, you will need a minimum of 4 GB RAM. If you plan on doing very large sessions, like orchestral session for example in HD, you will need a minimum of 8 GB RAM.
Hard drive speed should be at least 7200 RPM in order to keep up with large amounts of audio tracks being fed into your computer. Alternately, you can get a computer with a solid state drive, which is the preferred option if you are going to be recording large sessions in HD. While solid state drives are considered superior, they are often much more expensive.
Don't worry about how much storage space the computer has. While you do need some storage space, you need to have a high-quality external hard drive or a second internal hard drive to store your recording sessions. If you don't use an external or second drive, the speed of your computer may be greatly reduced.
Get a computer with a multi-core CPU. While the speed of your processor is important, you need a hard-drive with appropriate architecture for the best results. If you are going to be doing basic sessions, look for a minimum 1.8 GHz multi-core processor. If you are doing large or HD sessions, you will need at least a 2.26 GHz multi-core processor.