Are these good specs for a gaming PC?

If you're willing to drop that much cash, sure isn't a bad rig, and as a matter of fact, that graphics card will easily handle anything. I have an ATI Radeon HD 5770 which has 1GB of VRAM and I can play almost any game out there at this time. I, personally, don't like Home Premium and would upgrade to Professional if I was you. However, it is your choice, everything else looks great! Good Luck!