That all depends on what you are planning to actually do with the system. The OS requirements are just the starting point in choosing your build hardware and they are the bare-minimum requirements. Browsing the net, video editing (or other hardware hungry applications), and then there's gaming in an entirely different league of its own.
However, I personally would not choose a system for any reason that has anything less than at least a 2Ghz x2 core (Intel or AMD) and 4GB RAM. 1Ghz CPU and 1GB RAM would be way, way too frustratingly slow for me to work with in any capacity and Windows 7 is rather resource hungry in its own right.
And for video editing/gaming, I would not like anything less than 3-4Ghz x4 core CPU (Intel or AMD) with 8GB DDR3 RAM and a mid to high range ATI GPU (never been a fan of NVIDIA myself). Or even better than that, but that would massively wound the wallet.
Hope this helps you somewhat.