You could have a decent rig for that cash.
Cpu.. Intel 3570K OR 2500K
GPU.. HD 6950 Will run bf3 on ultra and they arent that dear.
Psu .. 700w for possible crossfire down the line.
Mobo.. Again just type in motherboard 1155 and take your pick in google but of course if you want crossfire you will pay more for x8 dual mode for gpus to run faster.
Ram.. 1333mhz ram is fine you can get that cheap now
Hdd.. Seagate 1tb would do. Prices have droped for hdd because of ssd's are getting more popular.
When building a pc its all about what you want its good getting advice but the best thing you can do is research cpus psus gpus and see what suits you. I jusy you tubed to see reviews and decided what i wanted from peoples experiance. I hope you have a great build mate.
What about downgrade the CPU to get a better GPU?, i think that way the build may last a bit longer, correct me if im wrong.
OP could save money by reducing CPU to, say, i5-3470 and losing aftermarket cooler, but that would reduce performance, and wouldn't free enough to jump to HD7970, or GTX670, which would give enough of a performance boost to make it worthwhile, plus the HD7870 overclocks quite well. I think this is the best balance, at the price point.