Win 7 ultimate 64 bit best for playing games, because it has direct x 11.
ALL versions of Windows 7 have DirectX 11.
In fact, EVEN Windows Vista has DirectX 11.
Why on earth would you think that DX11 was Windows Ultimate Exclusive? (Unless you work for MS marketing and get a commission for selling the OP an overly expensive version of Windows 7)
Home Premium x64 will do you fine. Check your video drivers are up to date before trying to play games.