The choice of screen is really down to personal preference, the size of cabinet you're building, and cost. Let's break this down into some areas for consideration and that might help you decide what you want / need.

Most of the games I play are from an era where the screens were CRT screens. Massively heavy and very bulky, these screens were the only option at the time. They almost always had a picture ratio of 4:3. Diehead retro gamers will always prefer these screens for the look of games as they have a distinctive display with scanlines and a certain glow to the image. You can imitate the scanlines and, while this is a compromise, it's not perfect.

The size and weight of a CRT screen didn't fit my needs. Older flat screens can be purchased which have a 4:3 display. Being on a budget, I searched eBay for computer monitors which nobody wanted and managed to pick up some great bargains. I went for 19 inch. One didn't even have a stand but, because I was fitting it into a cabinet, that didn't matter. I think I only paid about £20.00 for mine.

Newer flat screens are generally 16:9. These give a wider view. You can force them to display 4:3 images but you will end up with two vertical black bars on either side of the image. If you don't mind these bars, it is easier to find 16:9 screens but make sure your cabinet width is enough to accommodate it.

My screens only had VGA inputs. The Raspberry Pi has HDMI output. I purchased a converter to change the HDMI to VGA. This works well for the type of games I play. You lose some quality in the image but it doesn't matter on the older 8 bit games. One thing to bear in mind: my screen does not have speakers (the sound would usually play via the PC speakers of the attached computer) and, although HDMI can transfer audio, VGA cannot. The next article covers how I dealt with the audio.

My screen had VESA screw holes on the back for mounting to a stand or wall bracket. I used these to attach my screen to the cabinet but you might need to choose a different method if your screen doesn't have VESA mounting holes.

Finally, some other options. You can buy small screens which people fit into handheld consoles and some mid-sized screens might be good for a smaller cabinet. I've also taken apart an old laptop and used the screen. You need to buy an LCD Controller board specifically for your screen to get it to work but it's a good option if you have an old, broken laptop.