I'm not sure why the Radeon HD 5750 will not work, it definitely falls within specifications. Did you uninstall (probably should be done in Safe Mode) the GeForce drivers before installing the Radeon card? I've often heard this was an important step in switching between Radeon and nVidia.
Getting back to your primary question:
Your probably gonna want a GTX 460, 560, 660(newest generation), or better such as the 670 and 680. Since you have a budget of $200, ill hold back one generation and suggest the
GTX 560 for $150.
In case you haven't noticed, I'm an Intel/nVidia fan. I've nothing against AMD but have little experience with their products.