Monitor (computer screen) shopping results
(Q1 2016. Preferences are mine alone.)
Used vs new
Most older LCD screens are TN (twisted nematic) which has poor viewing angles and the colors change as you change angle. This gets on my nerves enough that I would choose a lower resolution IPS (in-plane switching) screen over a higher-resolution TN screen.
This rules out most of the cheap stuff on eBay. (Also, if you want at least 1920x1080, you were going to pay at least around $100 on eBay anyway, and $100 gets you a new 1920x1080 IPS screen e.g. on Amazon).
Other advantages of the newer stuff:
more energy efficient, so you’re saving $$$ on power (and on a/c in summertime; in winter, if you were using an electric space heater anyway, wasted power isn’t a waste)
usually has HDMI instead of DVI, a minor convenience if most of your other equipment is modern (HDMI-DVI adapters are cheap but one more thing to go wrong if the connection ends up being poor)
has LED backlight instead of fluorescent, which is a little more durable and less toxic and looks slightly nicer
If you want more than 1080 vertical pixels, or a touchscreen, on your IPS screen, then you’re looking at almost double or triple the price. Ways to get more vertical pixels: 1920x1200; 2560x1440 or more; screens that can “pivot” 90° to e.g. 1080x1920. (“tilt” is the rotation direction you use if you are too short or tall; “swivel” is the one you can also do by moving around the monitor on the desk.)
Resolutions higher than 1920x1200 are only supported by some computing devices’ graphics hardware. 1200x1920 is as well supported as 1920x1200 by these limitations, which I think chiefly are pixels-per-second limits in graphics cards, HDMI port/cable versions, etc. Sometimes the limitations let you do a higher resolution at lower Hz; sometimes not. Sometimes computing devices that look cheaper actually have better graphics hardware, so you have to look it up, or skip the expensive high-resolution screens, or get lucky.