Response time, as low as possible. I think 5ms is quite high.
Always look for a 'static' contrast ratio in the specs. You'll want this as high as possible. The huge numbers you see on the box are almost always the 'dynamic' contrast ratio. In short dynamic contrast means the backlight is dimmed when the picture is mostly dark. It's like turning down the brightness when you're looking at a dark picture, in other words you do not want that.
True LED screens do not exist AFAIK (or at least not on the consumer market). It usually means the screen has a LED backlight instead of CCFL tubes.
As for low resolutions, I have never seen a flatscreen that does that right. On most screens you can either set it to display it at it's original res (small) or have it streched out over the whole screen (blurry and some screens don't care about aspect ratio). Either use an LCD at it's native resolution or buy a CRT 😉

My new monitor will be a 30"at 2560x1600 (currently using a 24" at 1920x1200)

Only thing that worries me about the 30" is I game on a desk so dunno how well that will work with a 30" whereas with my 24" it's fine.

All the Dell monitors I've used have been fine with all the resolutions that I've tried. (mostly the only low resolutions I use are through DOSBox).

Don't buy a HDTV as a monitor if you want to run strange resolutions even a LCD excels over a TV for that. (Although the HDTV is ALOT cheaper so for modern gaming that may work for you).

My Acer 22 inch Widescreen supports native 16:10 mode, in this case 1680 x 1050 and has behaved fine for my modern and retro gaming needs for these past few years now.

Any Widescreen moniitor will be either 16:9 or 16:10 mode and do support many other non-widescreen resolutions too.

Last week I compared two Dell monitors, one with 50,000:1 contrast ration and the other 1,000,000:1. The higher ratio produced a better image, but the difference was very subtle. It's best to go have a look with your own eyes and see if it is worth it to you.

The old square LCD's are hard to find nowdays, it's all widescreen (in the stores. Second hand 17in screens are relatively easy to find atm). Hence I'm on the lookout for a second hand 18+ in square monitor all the time. Btw, I'm quite satisfied with my 32in LCD TV, even though it only does 1360x768 while giving a sharp image. And yes, it was relatively cheap, but I have to say some of the smaller "real" LCD monitors give an amazing image quality which somehow just looks better. I just wanted the biggest screen I could get for a certain amount of money, regardless of image quality, native resolutions etc etc. I can use a 19in CRT for that if I wanted to 😀

As my main monitor I have a Samsung 2232BW 22", scaling is as good as it gets for an LCD, even with old games. But I don't like scaling no matter what, and since used LCDs are so cheap, I got myself an old 15" IBM TFT monitor that does 800x600 and 1024x768 natively.

I believe this one scales pretty well:
http://hardforum.com/showthread.php?t=1387587

4:3 on this one give exactly the same visible size as my 21'' CRT(black 'bars' on each side).
Not checked the sharpness too much, but doesn't look too bad to my untrained eye.

I have a 1920x1200 24" pc monitor, I found that it works very nice in DOS 4:3 modes, the distortion is not that much like on the 16:9 monitors... I don't even notice it anymore 🤣

Just remember that you can't use a new monitor with very old video cards like Monochrome/CGA/EGA before you throw out all your old CRT's if you have any machines with those cards installed.