HP systems can work with linux OK, but you are porbably better of biulding your own from parts (or getting it built for you) over buying a desktop touchsmart.
BTW, if you are still after 'the best CPU' (not that such a thing exists, I agree with TobiSGD)
http://www.linuxquestions.org/questi...pu-4175426608/
Avoid the HP touchsmart series. They have slower CPUs than you can get for the same price if yuo build yor own, and slower memory, are very hard/impossible to upgrade, etc,..