I ran K2 on a laptop with XP Home with no issues
Laptop specs: AMD Turion X2 ML-54 (dual core), 2GB RAM, XP Home, 128MB nVidia card, odd's 'n' ends.
I'm also running K2 on a laptop with Vista with minimal issues:
Specs on this guy: Core 2 Duo 1.83Ghz, 2GB RAM, 128MB nVidia card, odds 'n' ends
My Intel seems to run a little less CPU strain with K2, but with the different OS (avoid Vista, avoid it I say!!) it's tough to make a direct comparison.
K2 has a little checkbox in the options menu for multiprocessor support.
XP Pro SP1 (or 2 if you use the system for internet) is your best bet for a stable audio- and audio-network-friendly machine, but XP Home will do just fine. Upgrades to Pro seem to be dirt cheap if you decide otherwise later.
i don't know if this site reccomends actual machines but it is very helpful for pc audio. (i'm a mac man with a dual athlon or something or other running K2, and it works great. i also have the RME 9652 audio card.)