Hey. Some people are gonna try to steer you clear from building your own machine by saying that GPU mining will soon become outmodded by ASICs, however there are still alternate cryptos (Feathercoin, Litecoin . . . ) that you can mine with your GPU that the impeding ASICs will not mine. An investment into $2000 worth of BTC should be a good investment, however if you have that kind of budget there is nothing wrong with having some mining fun as well.
You could build a machine that would hit between 1.5 and 1.9 MH/s (litecoin mininG) and 1.5 to 1.9 GH/s for bitcoin mining for your mentioned prices.
I'd look into snagging a simple MSi or ASUS board with 2 or 3 PCI-e 16x (size, not speed) slots. Grab a cheap Sempron 145, and make sure your mobo has the AM3+ socket. Unless you want to use it for a lot of gaming, consider going low-end on the hard drive and grabbing a 250GB magnetic, or perhaps a 128GB SSD. It's not a bad idea to leave a 2 or 3-gpu system out-of-box. My company sells mining units in PC cases to go with the idea of modular design as well as allowing for easy shipping, and easy deployment. However, if you are doing the build yourself, you may want to consider running your stuff out-of-box if you don't need to have it on a desk.
As for RAM, 4 GB would be plenty for mining, 8GB would convert it to gaming. For cards, if you intend to do scrypt mining at some point you may want to look into MSI Twin Frozr 3 GD cards, namely the 7950s. 7970s are a bit of a headache to do stuff with unless you really know your way around litecoin/NVC/FC mining
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For the PSU, get a PSU that is Bronze or above, the higher metals have better power efficiency. Always leave yourself headroom on your PSU, and try to plan your PSU for future plans (If you want to start with two cards, and decide to upgrade to three, it's nice to not have to fork over a bunch of cash to get your self another PSU! A good number is 300W per card. This is a bit high sometimes, but if you are doing good overclocks you can hit it. My 3x7970 machine draws 860-940W at wall and is an 80+SILVER.
Go cheap on the Optical drive if you intend to get one (unless you want fancy blu-ray stuffs), and make sure you get an extra SATA cable or two, you never know when a HD or optical won't come with one.
Good luck!