Depends on what you are going to do with it. Browsing the internet and reading email has a different requirement than playing games. Doing word processing doesn't need a beefy system, either.
Basically though you are looking at a 3 tier hierarchy. Low range with a Celeron CPU, mid range with a Core Duo or i3, high range with i5 or i7. 2 GB : low, 4 - 6 for mid, 8 - 12 for high. Only go with a 64bit OS if you require access to large amounts of ram (you probably won't). Stick with home editions unless there is a possibility you will connect to a domain (you probably won't).
*Yes, these are Intel CPUs and Windows OS. I have little faith in AMD, and you'll have an easier time with compatibility with Windows. You could do a Linux build and launch Windows in a Virtual Machine, get the best of both worlds...