The monitor I got (and still have) didn't break the bank, it was around $250 when I got it. Still going strong almost 6 years later, time flies! It is a Viewsonic 24", and 144hz. I noticed a large difference when I got it.
I'm not up to date on the latest models etc. However a few things that come to mind: Going from 60hz to 144hz gives the biggest improvement if I remember correctly, compared with going from say 144hz to 250hz (someone can correct me if I'm wrong).
The other thing that comes to mind is the input lag, which can vary quite a bit from monitor to monitor. Once you've narrowed down your selections, I'd look up some independent reviews on what the input lag is like on the monitors you are looking at. Older monitors and tvs can be bad for this, so you can see a big improvement going with something gaming specific.
Something else to bear in mind is I believe the larger the screen and the better the resolution, the greater the graphics card requirements. Worth bearing in mind if you intend on playing newer games and/or your card isn't great. Cod4 shouldn't be as badly effected, although I believe @KidSlayer! may still have ran into this issue at some point trying to play on something like a 64" screen?
I think @crimson upgraded to I believe a 144 or 165 last year and noticed a big difference, not sure which model he got, but perhaps he will chime in.
Maybe have a look here: https://www.rtings.com/monitor/reviews/best/by-usage/gaming
Their reviews consider/measure input lag.