Which edition of windows 7 is the fastest

No version of Windows 7 is really faster than the others, they just offer more features.
The noticeable exception is if you have more than 4GB RAM installed and are using programs that could take advantage of large amounts of memory.
In these cases, a 64 bit version of Windows 7 would be preferable to a 32 bit version (and should really be your default option at this point anyways9.

Unless you have a specific need for some of the more advanced management features, Windows 7 Home Premium 64 bit is probably your best option.