Do you have a monitor already? Do you have a keyboard and mouse? Is your budget just for the computer itself? If so, you have a great opportunity to be future proofed for years if the parts are purchased correctly, and you get plenty of feedback on what works.
I am skeptical on posting first about this because first, this is Neowin, and second, everyone has an opinion.
SInce you are a gamer, and want to fluidly play games, I would first look at video cards, second, processor, then third, memory. A fast hard-disk(s) is important as well...
Spend your money on the internals, and of course if you have money left over, which you should if done correctly, get a nice case!!
What else are you looking to do other than building a gaming rig? Are you wanting to over clock also?
Even if you do not have a good monitor yet, I still beliwve you can get there within your budget..
I personally have a AMD build. Great bang for the buck, but I also like Intel as well...
I would probably go for a Intel build with i7, nVidia Graphics, and as much fast memory you can afford, saving room for a fast SSD drive and a couple of fast secondary SATA III platter based drives for storage... If you have the money left over.. stuff it all into a sexy case, and enjoy!!