I think the minimum is something like a PII 500 Mhz, but I wouldn't recommend that.
I run it on a 700 Mhz PIII, but with dual 7200 HDD's and 512 Mb of RAM. I can usually get 15-20 tracks with effects without much problems.
I imagine almost any system you buy today would work OK, but would recommend that you go with dual hdd's (7200 rpm) and 512 MB of RAM.
If you plan on doing any Input Monitoring, you might need more a bit more power than the average bear.
Most important would be to make sure the mobo and chipset are compatible with the sound card you plan to use. That is where you are more likely to encounter problems.