As far as the consumer is concerned (as opposed to hardcore gamer), I think response rate is more relevant when it comes to gaming. From my understanding, nearly all LCD computer monitors do at least 60 Hz, which is fine for gaming. However, and this is a big one, response rates vary widely because they are not accurately tested the same way for all manufacturers.
Imho and to answer your question, most important thing is research from reviews and forums in choosing a gaming monitor
If you are asking from a hardcore gamer POV, then I really am unsure. 120 FPS at 120 Hz is awesome I am sure, but I haven't been there as of yet.