Hi there, I got a cheap Dell Optiplex 755 on eBay and had the same problem finding a video card to suit. It had to be a low form factor singe position card as there is just no room to fit a double slot card. I think it is the same situation with the 960. The .card I ended up getting was a second hand Radeon HD5570 (again off eBay for AUD$50.00) and it works like a charm. I've set up a multi-computer setup so didn't want to spend much on the machines. The Radeon is more than adequate for the Dell although I had to cut off a plastic *handle* thingy on the fan case so I could replace the side cover. I previously tried an HD6450 but the 5570 is noticeably better.
I would suggest looking for another computer rather than shoe horning something into the Dell. You will end up wasting a lot of time and money on a compromise. Another problem with the Dell is that the power supply is only about 250W and a big graphics card can pull over 100W. The Radeon only draws about 40W so is well within the machines limits.
I'm going to save up for a large tower or desktop that has loads of space inside and a big power supply so I can fit a huge multi-monitor graphics card. :-) I think your budget of $250.00 is way too low for what I think you want to acheive - isn't it always the way though - bugger!
