* PIII or AMD Athlon processor (PIV is a waste of money for this application)
* 256 MB RAM or more
* Preferably two 7200 RPM HDD's (one for system files, one for audio files, on two separate buses), but one will do fine if you don't need to squeeze maximum possible power out of it. The IBM 60GXP drives are highly recommended.
As for motherboards and sound cards, I'll let other people handle that (they know it better than I do). What I can recommend is getting a 24-bit audio card - it will be a lot less distortion to the wave files if you process them digitally as 24-bit as opposed to 16.
Also, if you're going to use MIDI in your compositions, using a SoundBlaster Live! as a synthesizer card works well and is unbeatable cost-wise. For higher budgets and higher quality, there is always softsynths as GigaSampler and it's equals.
The various gadgets inside a computer case will probably induce some noise in your recordings, at least if you use the analog inputs on your audio card. No card (that I'm aware of) has enough shielding to withstand *all* the interference other hardware gives. A solution for this is having an external AD converter - signal goes analog from the microphone preamp to the converter, digital from the converter to the digital input of the audio card. To make this work, you need an audio card with digital inputs.
Software is a matter of taste and budget. Most homebrewers I know are happy with the cheaper alternatives, Like N-track (
www.fasoft.com) or Vegas LE (
www.sonicfoundry.com).
Hope this helps, and please ask again if you have more questions.