If you have the money game on a 120hz monitor but I honestly think the refresh rate will not really make any difference in gaming, so I suggest you stick with the 60hz monitor.
Not true. From what I understand, 60hz limits you to 60FPS. 120hz, is 120fps. Although, most people cannot see a different after 60fps, so you should be fine. Anything below 5ms it should be good.