120Hz and up will do nicely. 144Hz is the baseline now, as that's what the majority of high refresh monitors support.
Anything above that is about how much money you're willing to spend for the premium. My personal advice is to get a monitor that is not "the absolute best" in one single thing but has shortcomings in other things, but to get something that's "really good" in many things instead of being "the absolute best" in just one thing.
If you've got the money to burn, and a store with a good return policy in case you get a unit with issues, a 165Hz IPS G-Sync is what I'd recommend. A pretty hardcore Quake player (Rocket Jump Ninja) got one of those (happens to be the same I'm using, which is an XG2703-GS) and has a review and his thoughts about it up on youtube:https://www.youtube.com/watch?v=KGjMiqG-6ys
However, it's not 240Hz. So it's not the ABSOLUTE BEST when it comes to refresh rate. But the 240Hz TN monitors can't compete in other things with it (resolution, size, colors.)
Not saying you should not opt for a 240Hz monitor. That would be a perfectly fine choice for Quake. Just mentioning that there could be other things to consider too
The views and opinions expressed in my posts are my own and do not necessarily reflect the official policy or position of Blur Busters.