It's not the firebox that needs a computer, it's your software. The Firebox is a firewire device, so your computer needs to be able to handle firewire, and then after that you're going to need to think about what program you're using when you're setting up your processor and Ram.
If I were setting up a new computer I'd try to get as powerful a computer as I could afford. An Athlon 64 with dual 512's of Ram (total of a gig) will do the job well, and the more Ram the better.
What kind of software and plugins you're using will determine how much processor you'll need, so tell us what you're using.
Jacob