The hard drive is pretty important too. My recommendation for a gaming rig would be to get like.. a 256mb or 512mb SSD as your primary onboard storage (that small because they run a little pricey) and try to keep its usage to a minimum, like literally for games only. SSDs are designed for you to be able to retrieve data from them at a substantially
faster rate then HDDs. Anything else you'd wanna store you should just buy a TB external HD.
I'm not going to do your budgeting for you, but this is a good place to look for your video cards and any other needs:
Newegg.com - Video Cards, Graphics Cards
Be aware, most of the high-end video cards nowadays are 13 inches, so you'll need a case that can fit that. Most cases can fit it no problem, but its just something to keep in mind.
More RAM is always better. Especially considering Chrome starts like 30 processes while you run it, and Firefox doesn't have a memory usage limiter. Neither do a lot of games nowadays, actually. I've got 8GB of RAM on my current PC, and it functions fairly well for my needs but I wouldn't call it a gaming rig. I still occasionally suffer from a short lockup when multitask on it too much, as a matter of fact. No forced restarts or bluescreens or anything awful though, just a short freeze before it goes back to normal.
I'm not gonna pick anything specific out for you but those are just a couple of recommendations based on personal experience.