First, let me say that it is probably best to hold off on the build until after the release of Ivy Bridge and the new generation of graphics card from both AMD and Nvidia. You could also save up a bit more in that time so you would have even more to spend when the time comes
Anywho though, I made a rough sort of build for you to consider if you want your computer sooner rather than later.
CPU: Intel Core i7-2600K 3.4GHz Quad-Core Processor ($279.99 @ Microcenter)
CPU Cooler: Cooler Master Hyper 212 Plus 76.8 CFM Sleeve Bearing CPU Cooler ($23.99 @ SuperBiiz)
Motherboard: ASRock Z68 Extreme3 Gen3 ATX LGA1155 Motherboard ($129.86 @ Newegg)
Memory: G.Skill Ripjaws Series 8GB (2 x 4GB) DDR3-1600 Memory ($46.99 @ Newegg)
Hard Drive: Samsung Spinpoint F3 500GB 3.5" 7200RPM Internal Hard Drive ($98.99 @ SuperBiiz)
Video Card: Sapphire Radeon HD 6870 1GB Video Card ($152.55 @ Newegg)
Case: Cooler Master HAF 912 ATX Mid Tower Case ($53.49 @ SuperBiiz)
Power Supply: Corsair 650W ATX12V / EPS12V Power Supply ($105.98 @ Newegg)
(Generated 2012-01-20 02:02 EST-0500)
First, yes, this will put you over budget, but this is kind of what I would see as your ideal build. First and biggest thing you could do, is that if you're not going to be doing much video editing, you can get along just fine with an i5-2500k. That would shave off $100 right there. You could also drop down to a 6850, but especially if you're wanting to play BF3, I suggest the 6870. So you or whoever else jumps on this thread can just take this list as a sort of starting point if nothing else.
Remember though, I would HIGHLY suggest waiting for Ivy Bridge and the new GPUs instead of continuing on with the build!
The simplest way to put it is that the Intel Ivy Bridge processor line is that it is a die shrink of the current Sandy Bridge processors ( which include the i3-2100, i5-2500k, etc). I can't give you exact numbers, but what this means in practical terms is that these new line of processors will get ~10-20% boost in processing power, MUCH better integrated graphics (which won't apply to you though since you'll have a discrete card), and less power draw to do it. The unlocked processors will most likely overclock even better than the current Sandy Bridge line too.
I wouldn't count on the Sandy Bridge processors going too far down in price after the release of ivy Bridge though. If you look on newegg, even older processors with outdated sockets like the core 2 quad go for $240. So, it's not an idea of waiting for the new i7 or i5 because it will save you money on the current ones and more about spending roughly the same amount and getting a better product.
At this budget its better off to get a 2500k rather than a 2600k although you think of video editing. This build has everything you need including the OS and you can't really cut down on anything to make room for a 2600k. EVO is best bang for buck, the hdd is the lowest priced reasonable size hdd, case is pretty cheap without going too cheap, ram is the lowest you can get for 8gb, a cheap non-modular psu by a good brand that will give sufficient power, and mobo is a low priced z68 mobo with good features and without sacrificing quality. So with the money after all this you can spend it on graphics and cpu. The 6870 and 2500k will offer the best balance with the remaining money IMO.