As usual, the answer is, it depends...
Firstly you need the monitor to match the number of pixels the graphics card on your computer is sending out. That is probably the most important thing otherwise you will need to reduce the computer graphics definition, or stretch the graphics to fit the screen.
Do you want to use the monitor for photo editing? Then you will need a monitor that allows you to adjust the colour settings to match closely what you will be printing out.
A monitor for action gaming requires higher speed, so a hundred hertz refresh rather than the fifty or sixty hertz more commonly found. Video fidelity probably isn't quite so important here.
Then there is the final and most important question, how much do you want to spend?
As an aid to making a final decision, try and find somewhere you can see various monitors in action, side by side. Some you will be able to dismiss out of hand at a glance, others may appear almost identical and the difference will be in what level of control you have over colour rendition and how easy it is to store and switch between different settings.
OLED displays are vibrant with very dark blacks, but tend to be more expensive. Older technology TFT displays are still very good. Look for screens with the widest viewing angle. Can you still see the screen clearly from the sides and above and below. Do the colours shift or become bleached or dark? Move on to the next screen.
Anything with a screen panel manufactured by Samsung will probably be good.