Without going into specifics, the shortest way to get a good screen is probably to buy an IPS display (it's barely more expensive). Pretty sure all IPS display are at least okay.

The cheapest displays are TN because it's cheaper to manufacture, sadly that technology has very bad angle of vision, move a feet to the left and another feet and you'll see the image looking different, it also has a more limited rendering of colors. Not great.

Typically you realize how bad a screen is when you try to calibrate it (looking at a few pictures is enough, no need for expensive equipment). With a really shitty screen, you will notice that the display literally cannot render half the colors.

For example looking at a picture with 16 shades from pure white to pure black, the 4 first levels of white look the same.

Typically that's the part where you have to adjust brightness/contrast until it's showing a difference. If you have a really shitty screen, there's no settings where half the colors will render. The example above being extremely skewed toward bright white will slowly destroy your eyes, being too bright and removing details/contrasts.