The VS247H-P is a perfectly good monitor. It supports a maximum refresh rate of 75 Hz. How much actual FPS you could get depends on your hardware and what game you are playing, but the maximum you would be able to see is 75. You would need to use the DVI connection to get 75 Hz at 1080p though, since HDMI won't support anything above 60 Hz at 1080p.
If you are really into competitive shooters, you may want to go with a 120/144 Hz monitor (if your hardware can render that many frames) for the smoother visuals. So something like the ASUS VG248QE would be better (only for shooters)
http://www.amazon.com/VG248QE-24-Inch-Screen-LED-lit-Monitor/dp/B00B2HH7G0/ref=sr_1_1?ie=UTF8&qid=1382735075&sr=8-1&keywords=asus+vg248qe
But in general...