I am not aware of single entry-level GPU (one you would expect in prebuilt desktop) capable of handling three monitors with identical connections, so you probably have to get a pre-built desktop and upgrade / swap the video cards, or use something like
Matrox TrippleHead to split single DVI-DL signal over three DVI monitors.
But with the price of TripleHead around $300, you will be probably better getting a desktop with built-in graphics only, they slapping two mid-range GPUs. With $500 going to monitors, and another $400-500 toward GPUs, this leaves $500-600 for your desktop - quite good amount.
I will others to comment on actual build, GPUs are not my playing field