I believe the best FM1 is the A8-3870K which might cause a problem for some multiplayer games because it's individual cores are still weak, although, it is a significantly better CPU than the A4-3300. It will bottleneck the GPU but most of the time you should still have acceptable frame rates.
It looks like you have 2 options. Buy the GPU, power supply, and the A8-3870K and hope it doesn't cause any problems during the games you play (especially during multiplayer), or basically just build an entirely new system and go with a socket that is actually good for more intense games like the LGA 1155 or AM3+.
If you mean the latest High End games and you aren't on much of a budget, I'd get at least the 7850 but if money isn't really that big of an issue at all and you want to max out their graphics or get rather close to it, I'd take it up a notch or two and go with a 660 Ti, 7870, 7950, 670, or 7970.
If you mean mainly MMO's, you won't need anything more than a 660 Ti or 7870 (as they should have 60+ FPS in most situations with maxed out graphics) if you didn't want to spend extra for something better. The cheapest I'd go is the 7770.