Quote from Bolimomo:
Many seemed to recommend Dell desktops. All I want to say is: check the available expansion slots. If you have only one PCIe X16 slots (as this is common with most desktop models these days), to drive 3+ monitor you would need to purchase a quad video card. And quad cards are expensive. Can be looking at USD $500 for the video card itself and this will blow your $1000 budget right out of the water. Though perhaps you can use a USB-to-VGA adapter to drive a third monitor with a dual card. Just something to think about.
Not really - the PC i'm selling only has one PCIe x16 slot but has several PCIe x8 slots - you can buy an NVIDIA NVS 290 PCIe x8 or X1 dual monitor card for $60-$80 on ebay.
I'm giving the machine away with any old video card but its NVIDIA so it would be compatible with any NVS card and someone could run up to 6 monitors for an additional $150 (ebay prices).