Okay, I hope I haven't confused you...
Anyway, you can get a 60Hz with an IPS panel (IPS is better if the monitor is well-built).
I de on't have time to do any research, but this one isn't very expensive and the few reviews here arfavourable:
http://pcpartpicker.com/part/hp-monitor-23xi
I have an NVidia card, and use Adaptive VSync for most games (you can Google that if you have NVidia).
I generally use VSYNC ON because I can't stand screen tearing so I prefer to have the FPS over the refresh rate at all times. If you have VSYNC ON but can't output above the target (in this case 60FPS) you get a very quick, annoying stutter due to the mismatch.
Thus, I use Adaptive VSync and carefully calibrate my game settings so I rarely, or never, drop below 60FPS. Adaptive VSync will simply turn VSYNC off if you can't output 60FPS so you get screen tearing as per normal with VSYNC off but don't get the stuttering.