You should be able to get a Dell with an LCD and a warranty for under $1K. I don't have much experience with HP desktops. I would stay away from Gateway and no-name Walmart cheapies. As mentioned before the power supply is critical and the really cheapo brands will come with a PS that I wouldn't trust to power a flashlight.
As far as build your own, that ship has pretty much sailed on the lower end market. The margins are so thin that only the big players can build a really cheap-yet-decent computer. I build my own but I am exacting about each piece I put in. The cost of building a pretty high end machine has remained constant for me at about $2K since 1998. I'm about to yank the guts out of my current machine and upgrade most of it. The old stuff will upgrade a server. But it will still cost me $1200 to upgrade the Big 5 (Mobo, Memory, CPU, Video card, HDD), the bulk of it going to the vidcard and CPU.
