Getting a gaming PC, on a budget?

I'm getting a new PC for up to $600ish dollars soon. It would be fantastic if it could run something like Minecraft or Gmod on high, and something like Gta IV or Battlefield good on any settings, preferably higher ones. I would not mind building one, although a pre-built one would be easier. It also must have this specific graphics card, Gigabyte GeForce GTX 750 1GB Video Card, or one very similar to it as I'm playing on two HDMI monitors.

There are countless options for building a gaming PC with those specs at that price range. However, keep in mind, if you are new to PC gaming there are many other accessories that you will need to get besides just the computer itself. You might need an HD monitor, gaming keyboards and mice, and your Windows operating system.

If you really can only spend 600$, you might need to make some compromises. For example, you can avoid getting a DVD drive, since almost any game you can download off the internet these days. In regards to specifics, I recommend making a post on reddit's buildapc, there are tons of people who are experts on building gaming PCs that would be willing to help you out.
http://www.reddit.com/.../buildapc/

In regards to a prebuilt PC with a GTX 750, that might be a bit tough to find, since it is a relatively new card. I search around online though.