Your monitor at 1920x1200 is technically 1200p, not 1080p. Since it is [slightly] above 1080p (which is called Full HD) then you of course have a Full HD monitor with a little better vertical spread than 1080p and a slightly different aspect ratio. Not much, but a tad more. Some folks prefer the extra real estate of the 1200p. As far as the preferred gaming monitor right now however, it is a 1440p or more accurately 2560x1440. This is because:
a) it is a pretty noticeable jump visually from 1080p
b) and it can be made to have response rates that are below 4ms, to prevent that ghosting effect, and it is available in IPS/VA screen types, which produce much better and more preferred colors and viewing angles than the TN screen type monitors which are available everywhere
c) not as pricey as 4k
d) can be ran with less graphical muscle and achieve the magical 60FPS on high settings
And then there is UHD. So technically there is UHD (commonly and incorrectly called 4k), and then true 4k. UHD is actually 3840x2160 - but "true 4k" is a resolution defined as 4096x2160 pixels. This is widely used by the film industry but rarely seen on computer monitors/TVs (LG does make one though). Both UHD and 4k produce a fantastic image (UHD/4k are so close to each other that it's hard to tell a difference between them), but they both require so much graphics card muscle that there isn't a perfect single card solution just yet. A GTX 980 Ti 6GB, or of course a Titan X can do the job with settings tweaked down a hair, but the problem is that you need a bigger screen with "4k" (yes I'm just going to call UHD and 4k - both "4k"). There are scaling issues. Images are tiny at the native resolution. You need a 27" at a min. and preferably over 30". Then the screen type comes into play. You want that quick response rate to prevent gaming ghosting (below 5ms), but that tech is super expensive and hard to make right now on anything other than TN panels. That's why the majority of 4k monitors are indeed TN panels (inferior, cheaper, with better and low response rates -even as low as 1ms). But on an IPS panel (which is what we all want for gaming) you see 6ms, 7ms, 8ms or higher response rates. Not great for gaming.
I personally use a Dell 27" IPS UHD/4k P2715Q 3840x2160 monitor and I love it. I have an MSI (overclocked) GTX 980 TI Gaming 6GB card. This monitor has a "fast mode" and it drops the response rate from its default 9ms to 6ms. I find it is just fine and really don't (if rarely) see any ghosting. The picture is absolutely stunning on games like BF4. It will make your jaw drop the first time you see it. I can run all ULTRA settings across the board and just cut back on the Anti-Aliasing and maintain well over 60FPS. The argument about AA is that the pixel density of UHD is so tight that AA is unnecessary. I can attest to this. I've tried it both ways and you really are hard pressed to see a difference. I have to say that I was a little worried that the Dell 4k would not be so great for gaming (I do photo editing so I was prepared to use it solely for that). But after having both a 1440p 27" ASUS monitor, and now this 4k Dell - I have to say I have no regrets about getting the Dell. It is absolutely the best monitor I have ever had. And gaming on it is just fine on it, if not outstanding using DP with NO ghosting, even on FPSers. GTA V looks great BTW too and I stay around 50-60FPS with 90% of settings maxed.
Your choice, but do some research on your own before you buy. Just remember -you will need a high end graphics card, or you'll not be happy. And I wont even go into to the G-Sync/Freesync and that tech. But its coming and will help with the constant and steady frame rates.