Not sure of the minimum, but I can run it off the oldest laptop I have. Im running off the HD install on a 1.8ghz Celeron M, 512MB RAM. This is fine for cracking WEPs or capturing handshakes but I wouldnt try to brute force anything on it. It is also very easy to crash it if you run too many GUIs
My advice would be to HD install it on a slower computer and stick to command line. If you have the horsepwoer then go ahead with the USB boot. Using a live CD for anything other than installation/emergencies is about as frustrating as trying to teach a paraplegic to ride a unicycle.