I have a fourth option for you:
Buy the parts and take it into your nearest computer store, who in general will have an assembly service where they'll build it for you. You save money, and you don't have to worry about building it yourself.
In the way of recommendation for parts, with your budget you could get the king of all gaming PCs, but I'd go for something a bit under but still affordable.
CPU: i5 2500K
Great CPU for gaming. Seriously, you won't need anything more unless you're planning on playing hardcore Dwarf Fortress on a 16X16 embark and digging into hell, or Sins of a Solar Empire late game on a massive multistar system with tons of strike craft. In that case I'd get an i7 2600K, but otherwise definitely not needed. You could get just an i5 2500, but the K is good for overclocking - which is a good way to get some extra speed from your CPU if its bottlenecking you somewhere, which is unlikely but possible dependent on the game. I wouldn't overclock too much however without liquid cooling. If you're not at all interested in overclocking, just drop the K and get the basic model for cheaper.
Motherboard: ASUS P8P67
Not exactly a great motherboard, but it'll get the job done well enough. Definitely compatible with the i7 2600[K], and I'd assume compatible with the i5 2500[K], but maybe not so I'd check it. Its got some issues, namely the PCI-E ports are too close together so despite having 4 or so, if you get modern graphics cards you can only put two of them in SLI/XFire as the cooling units cover the other slots, but it works for me, and was reasonably affordable when I grabbed one.
Graphics cards: Minimum 560Ti, but with your budget I'd get 2 GTX680s and put them in SLI.
The 680s are just powerhouses, and two of them in SLI will cover all your graphics needs for ages. Not sure if there's a 1Gb model, but there is definitely a 2Gb model - which is what I'd say to go for anyway.
Hard Drive: An SSD of some sort.
I've got a SanDisk one with 550Mb Read speed and 530Mb write speed and 240Gb capacity, and it works well, but there's probably better ones on the market, or worse and cheaper ones on the market too dependent on your needs. Either way, an SSD is amazing for the speed it provides. Even with it almost full ATM mine boots up Windows in under 10 seconds.
Monitor: I'd look into a 2560*1440 monitor.
They're not the highest resolution out there [I believe the 2560*1600 monitors hold that], but it is far more affordable and nearly as good. You can get one for $300-$350 off a brand known as Yamakasi, shipped for free from South Korea. Myself, and everyone I know who has gotten one, will verify they work, though I have heard the occasional complaint about them - though often nothing major. You could get one from a well known brand instead, but they are generally far more expensive.
Case: Any full tower with a decent number of fans.
Really, any full tower with >4 fans is something good to go for. Just be sure to fully deck it out with fans for good cooling - with two graphics cards you might end up needing it. I'm using a Thermaltake Chaser Mk-1 that I got off a friend with full fans, fan controller and blue LED light loadout for $100, though they're generally a bit more expensive than that. There are better cases out there too that you might want to look out for, though I haven't researched too much in that field.
Power Supply: 750-1000W modular.
With two graphics cards you'll need a lot of power. Without checking the power specs for the 680s I'm not sure exactly how much, but 1000W is a safe bet. Modular you'll want to ensure you can plug everything into the power supply, and it also allows you to better manage cables through not having a lot of useless ones dangling around. Try for a good brand too, as some brands can give you somewhat dodgy power supplies, which is bad news for your rig.
For the rest of it its not that much of an issue. Hell, half of that isn't but I thought I'd put it up anyway. I'd go for 16Gb RAM just 'cause. 4 4Gb sticks should fill out the dual channels in the P8P67, and is reasonably affordable as well. You could easily run anything with 8Gb, and get faster RAM that is slightly more expensive - which is probably the better option if you're not going to be doing masses of multitasking with your PC, but I went 16Gb 'cause I tend to multitask a fair bit [Around 16 Chrome pages open, 4 Windows folders open, 2 games, 1 game's map editor, several word and notepad files, 1 powerpoint and a few other bits and pieces dependent on the day, 'cause I might just alt tab and decide to look at one of them at some point >.> {I'm terrible, I know}].
Either way, people here could probably give you better suggestions than I have, but that should be a damn nice build for your price range. Just buy the parts and get your local tech store to assemble it for you, if you don't want to try to yourself.
Have fun with your new computer either way.