I like building my own PC just so I can customize certain components i.e. video, RAM, HD, etc... But if I was on a budget looking for a decent deal, I'd get a Dell system on E-Bay. In fact I did a quick scan of systems in your price range and included a link of a particular system.
Dell System Link on EbayFor $770.00 shipping included you get an Intel 3GHz with HT, 1GB RAM, 16x DVD-RW Dual Layer, plus a second CD-ROM, 250 GB hard drive, WinXp Home Edt.
If you did a more thorough search, you may even find a better deal. Though this system is'nt bad, it comes with the operating system (winxp), which is usually an extra.
The only bad points I saw was the integrated graphics, which I'd recommend upgrading. That you can always do later. NOTE: If you do decide to go with a system like this, e-mail the seller to make sure the motherboard supports AGP 8X video cards, if not look for another system.
Everybody will go on and on claiming this component is better than this and that, but believe me I built dozens of systems, high-end and low-end, and sometimes the differences are minuscule. Just go with a high-end video card, that you don't really want to skimp on.
If your not looking to OC your system, then Dell is fine. Plus you'll get a warranty for a year, which you could always upgrade.
The one thing I always loved abouts Dell is their cases, which are super quiet. Customised PC's always have bad air-flow and rely on 5 different fans making them sound like a vacuum cleaner.