At that resolution the monitor will not lag but you may need to double up on the 580s.
The two issues are colour reproduction consistency (IPS helps this) and smoothness of the monitor in production of changing images (higher frequency helps this)
Most gamers would like both but you will find that there are only one or two that do this (Mitsubishi).
If you go 2560 x 1600 you will find that a 120hz monitor will not help due to you having video lag before the monitor even processes it. The monitor will also make your movie and video watching pretty unpleasant so only consider this if you are an avid gamer.
My opinion is that IPS will be the better choice. The colour will be brilliant in gaming (you sacrifice a little response time), the movies will look amazing, your photoshop, etc will be great and you will have a nice viewing angle.