First off, I do not think that the GTX 470 would be on the list of things to get if you want a 'best game rig as cheap as possible'.
The GPU will very much be decided by both your requirements, as in what games you play, and what resolution and settings you play on.
Furthermore, it is very hard to gauge what you should get if there is no budget to go by. We could take the processor and the GPU as staples and build around that, but that will just be a generic build with solid components using the weekly deals and what is known to be bang for buck hardware in general.