If you have a GTX 560 ti, it should tear through most games pretty well. I wouldn't worry about screen resolution too much.
But with a budget at $100-$120, you won't be able to get a 1920x1080 resolution monitor.
EDIT: I take that back! I think I found a monitor that was built specifically for you
21.5" with 1080p and a 3-year warranty at $119.99 free shipping. I'm kinda tempted by this one myself...