For a 20'' monitor and $200 budget, You will be absolutely happy with the performance of 5750 HD or may be 5770 HD.
Provided you have more budget and want to play games at maximum settings, I would strongly recommend you to go with 5770 HD.
It is around $160. And performs on-par with 4870 HD and GTX 260, Adding DirectX 11
I would again say that go for 5770, If you want to play games at maximum settings at your monitor.
Buying $130 5750 will be a good choice, but may be you won't get the the chance to maximize settings in CRYSIS and coming games
Once again, I would say you to for 5770 HD