I'm not aware of any precise minimum other than being able to run windows 7. If you want to run VC and run XBMC etc I think an i3 would be a safe minimum, but VC will run on a single core atom. The one I tested was a netbook with 2 gig ram, and it was and older version of VC but it should work. I think there is still a YouTube out there.
I still like to have some breathing room though. The number of commands and the size of your payload XML files will determine the actual needs. With plenty of ram, if VC is the only thing running, response time will probably depend as much on the quality of your mic as your CPU speed.
