I just started up the campaign for BF3 and I'm getting around 15-20 FPS at most. This is on highest settings.
That's your problem, aside from a 5400 RPM hard drive. Sadly, BF3 is quite a demanding game. I have a similar build to you I would say, considering there wouldn't be much an FPS difference from 5400 --> 7400 RPM, don't quote me on this though. My graphics card is also on par with yours (the 6850 and the gtx 460 are nearly identical in terms of performance), and we are kinda there on cpu's with mines only being slightly
better, it's not OC'd yet like my signature says.
Like trotter said, medium settings is what you want. I play multiplayer at 40-50 FPS, and it dips to as low as 35 in high-paced combat. And, I play on high settings, not the highest like you said, you just can't run it smoothly with that build and maxed out settings.
Test it out on medium, I would say you would have at the very least enjoyable results. But for the other games, you should be fine running them on atleast high, maybe not maxed.