The reason I asked about the games is that if it was more in the vein of counter strike, where milliseconds count, it might be more critical that your response time is as low as possible (higher Hz). The games you play, which are quite similar to those I play, are more graphics-focused, in my opinion. I think, therefore, that a higher resolution monitor would be a better investment for you than one with a higher refresh rate. You're gonna notice the difference going from 1080P to 1440P a lot more than the difference of 60Hz going to 120Hz.
Now, as we've mentioned, with the overclockable Korean 1440p displays, you can kinda have the best of both (or all 3?) worlds. 1440p resolution, overclockable to at least 96Hz, and only $300-400. I more than understand hesitation to go that route, though, so leaning towards the Asus (or other) 1440p display would be more than acceptable.
Your budgetary restraints do limit you from getting a native 120Hz 1440p, however, so I would just rule that out completely from your thinking. Thus, I think you have 3 options:
-Korean 1440p 60Hz (OC'able up to 120) for ~$350
-"name" brand 1440p 60Hz (not likely OC'able) for ~$450-<your max budget>
-1080P 120/144Hz for ~$200+(?)