Yeah, so your GPU is holding you back rather badly even for Skyrim. Look into a 6gb 1060, or 480, when you get the chance
CPU could be better, but Skyrim isn't the most demanding game, so I wouldn't put priority here. You may want another 8gb ram if possible.
Your biggest problem may turn out to be connectivity. Most monitors now are displayport, and I don't think your GT620 will have that. You may find you have to buy an adapter - specifically an "active" adapter - which will add £30 or so to the purchase. I'd be inclined to buy the screen and the GPU at the same time so's to avoid that...
Regarding refresh frequency (hertz, Hz), it limits your maximum fps, and it's largely subjective as to what's good enough. Some people have no issue at 60Hz, others insist that games are rubbish below 100 or 144. Personally I find that 60 fps on a 60 Hz screen is perfectly acceptable.
G-sync and Freesync are adaptive-sync technologies designed to reduce the perceived stutter of low fps. To explain; if a monitor is listed at 60Hz, it means the screen refreshes at 60 times per second. Not "up to 60" but straight 60. This means that if your GPU is delivering, say, 45 fps, then for every three frames that are generated, the monitor has to display
four. Over six frames and eight refreshes, they display in a pattern of 1-1-2-3-4-4-5-6. You'll perceive these double frames as a stutter, even though fps is technically reasonable. Any time your GPU isn't putting out 60 fps or above, you'll be getting frame duplication like this. Adaptive sync allows the monitor to lower it's refresh rate, so that you feed it 45 fps, and it refreshes 45 times per second with every frame getting the same display time and no duplicates.
TLDR: g-sync and freesync make games smoother when you can't drive them at the monitor's refresh rate.
Response time (miliseconds, ms) is the time taken for a pixel to fully change from one colour to another. It's also massively overhyped and misused. 1ms response implies 1000fps... and the technology used to provide it often results in poor colour accuracy. Imo there's nothing wrong with 6-10ms response times for most cases. Outside of 144Hz screens, there's really no need for ultra-low response times.
If you're really unsure what you want, it seems like the majority of people are happy with a 27" screen at 2560x1440 resolution, so that's probably where to aim. They're common, and there's a huge range of prices/performance to suit your budget and needs. Speaking of which, let us know your budget and we'll be able to suggest something
