I was thinking the same thing... CRT or GTFO
Also, screen size is important, but what also matters is how close you are sitting to it. These games are designed to be sitting directly in front of a 25-27" monitor that is tilted backwards a bit. Giant screens are going to be a disadvantage because your field of vision is not going to be able to really process everything at once. Many of the best players use small screens because they can see everything at once without adjusting their eyes much at all. The larger the screen, the looser the controls are going to feel, that's a fact.
As for how to play, well there have been a few good suggestions and I'll reiterate the important ones and add a few:
Lots of practice with the SAME GAME is key, but also playing a wide variety of games will help you improve faster as well. It's a catch22 but it's absolutely true. Different games teach different skills, once you gather enough skills, apply them all to a game you like AND STICK WITH IT until you see drastic progress.
Learn and apply the different techniques such:
Micro dodging - weaving with small dodges in between patterns, focus on the empty spaces between the bullets... if you look at the bullets, you'll fly into them lol!
Macro dodging - swooping around an entire pattern all together
Tap dodging aka streaming - tiny taps in the same direction to have bullets miss you by only a small distance
"U-dodging" and bullet herding - how to position yourself to control where enemies will fire
Panic Bombing - if a game has bombs, learn to use them right before you get hit. many players don't know how to do this and die again and again with bombs in stock.
Quick-shot - many enemies can be killed faster the closer you are to them due to rate of fire. learn how to be aggressive when the game allows it.
Those are some of the important skills, feel free to ask questions.