I would recommend 17" for most content that was made before 2000, and 19" and larger for more modern content. Anything that's 640x480 or lower will look better on a 17" in my opinion.
Also, I tend to avoid flat screen CRTs because of geometry and focus issues, and the picture doesn't look as immersive because of their thicker glass. Similar to a tablet with an unlaminated screen. It's not a hard rule but you should at least know about these problems.
As mentioned Sony Trinitron monitors are the best, often very sharp, vibrant colors and great brightness thanks to the aperture grille tube. Diamondtron tubes are the equivalent from Mitsubishi. But it doesn't have to be aperture grille, a good shadow mask tube can also look great and authentic for older content. Samsung monitors are top tier, know to have some of the sharpest, most vibrant picture and constantly scoring high in magazines. But don't just go by the brand of the monitor, there are a lot of brands that didn't actually produce their own monitors. It's more important who the original manufacturer is.
Things I personally look at:
- Dot / Grille pitch. 0.27mm is poor, 0.26mm okay, 0.24mm razor sharp. Often directly correlates with the tier of monitor (cheap to professional/high-end)
- Production country: Anything made in China / Taiwan is often bottom of the barrel, anything from Japan is high quality, Sony, Mitsubishi, NEC, Panasonic. Korea is most likely Samsung or LG. If it's an aperture grille monitor, you can also spot it by the screen shape (it doesn't curve towards the top and bottom).
- Screen coating / tint: The darker it is, the more expensive a monitor tends to be, and the better contrast it will have. But it will also wear out faster because it has to be brighter to shine through the coating.
- Horizontal scanning frequency, should be at least 96 KHz for a 19" and 80 KHz for a 17". But I would always willing to compromise on that if the picture quality is nice. You don't need to play everything at 100 Hz, especially older stuff.
- Scratches on the screen coating. Annoying because once you've spotted it, you can't unsee it, especially on more static pictures. It's also impossible to repair.
- If you have photos of the running monitor, look for geometry problems such as warping and poor linearity, also poor brightness/contrast, especially red. Grayish whites, poor highlights and weak red color = worn out tube. A sign that the brightness is good can sometimes be when bright areas have a little "bloom" around them, bleeding into adjacent areas. Run the same content on your own monitor to have a comparison for how it should look like.
And lastly, the best tool for getting a feel for what's good and what's not is browsing through reviews from old magazines. You can find a ton of them on archive.org. Search for a particular monitor model using the "search contents" checkbox, and it will show you magazines that reviewed it.