That is the million dollar question, which contains many variables. What software are you running, what operating system, do you record full bands, orchestras, etc.
Setting up a digital audio workstation can seem very daunting, challenging and expensive. You may be able to get by with that old Compaq 1.4, 512 RAM and 40 gig hard drive. But if you start loading a ton of loops and samples, VST instruments, etc. that hard drive is going to be full in no time.
My philosophy is bigger is always better. In my opinion, your most important piece of hardware in your studio is your computer. You may want to splurge and spend some extra money up front. It all comes down to processor, memory and hard drive, everything else is just not that important, with the exception of soundcard/interface. Quiet fans and drives is also an important consideration, but that's another story.
In a perfect world I would find something with multiple processors, getting the fastest processors you can afford. Memory is the same way, get the most that you can afford. If your computer can handle 8 gigs, get 8 gigs. Hard drive is the same, get something with 2 500 gig drives or better yet 2 1 terabyte drives.
When shopping for your digital audio workstation think about the future. Get something that you can upgrade. For instance, don't buy a pc that can only handle 1 gig of RAM. That thing will be outdated next week. If you can only afford 2 gigs of RAM right now, that's fine but make sure your computer can handle at least 8 gigs in the future when it comes time to upgrade.
Recording music takes a lot of horsepower and space. Make sure you get something that can handle it, and make sure it is expandable.