64 bit operating system and routers

Doesn't matter, the OS of any wired or wireless client is oblivious to the router. The OS has no clue what type of device lies at the other end of its wired or wireless client adapters, nor does it need to. So just buy the router you want.

Having said that, seeing as how this is the wireless forum, perhaps you meant to say "wireless client adapter", and if that's the case, then OS compatibility is a valid issue.

http://www.microsoft.com/windows/compatibility/windows-...

I have no idea which is "the best", but that's a starting point.