The answer to what phone should I buy usually starts with questions about screen size and budget. Its the first thing would be buyers should decide. The more selective among users then proceed to ask about the quality of that screen resolution and panel type.
Today we want to focus on the latter LCD or AMOLED? The battle seems to be over as Samsung has been pushing AMOLED for years, Nexus/Pixel have been on and off and on again, LG is jumping ship, even Apple is on board.
Is that the end of LCD? Unlikely, there are some high quality panels (like the ones used on iPhones) that are bright, legible in sunlight and offer excellent color accuracy. Its a meme that AMOLEDs have oversaturated colors, but in reality its a matter of tuning.
Samsungs Super AMOLED flagships top the charts on Basic mode yet few people switch to that mode and prefer the extra colorfulness of the less accurate modes (despite all the complaints in comments).
Then there are Quantum dot displays like Sony has been using for ages and Samsung is putting on its top TVs yes, the AMOLED king on phones chose another tech for TVs. They are brighter for the same power usage and have a wider color gamut compared to conventional LCDs.
Wed love to put e-paper among the options, however eInk never delivered on refresh rates and colors and the LCD-based Mirasol by Qualcomm folded. MicroLED could be a thing of the future, but not today.
So well leave the fourth option as Dont care, as long as the quality is good.