You've said money was not the limiting factor, so don't go for an FX 4100. Note that no one criticized your choice of the i5-2400 (I think I might have planted that one in your head, actually), because it's solid for non-overclockers. The FX 4100 is not. In some games it will lose to an A8-3850:
http://www.legitreviews.com/article/1766/13/. Wow, just wow.
As for the GPU, I'm actually going to go with the GTX570 here. But not because of MSAA, which the GTX570 most definitely
cannot handle at 1080p. Rather, it's because the GTX570 is slightly cheaper and offers more consistent performance than the HD6970, as shown in the apples-to-apples [H] comparison linked earlier:
http://www.hardocp.com/article/2011/11/22/battlefield_3_multiplayer_performance_iq_review/4.
If you find an HD6970 for the same price, I'd go for it just because it's slightly faster in most games.