I have 3 CRT TVs (non-pvm, 2 after Y2K with s-video) and 2 CRT PC Monitors (one that can do 1080p from ’04 and one from ’95 I use with my MiSTer).
I mostly try to stay period appropriate since, yes, the smooth motion and sharp image you get from a CRT on 240p/480i signals was the intended design target and therefore looks the best (with good hardware), sometimes using the physical electron beam phosphor bloom or composite rainbow to compliment the pixels. With my MiSTer I use direct video 240p line doubled to 480p over VGA on a PC monitor and inject scanlines. It probably looks a little too sharp to some purists but I like how I can also quickly change the output to a scaled 1024×768 for easier compatibility for systems with weird resolutions instead of using one of my s-video TV sets (I use those with my real consoles - none are RGB modded thanks to the MiSTer).
I do use my 1080p CRT PC monitor with my PS3 and 360 though since most of those games run sub-720p (I set the output to max at 720p for improved frame-rates as well in some unlocked games). It helps to scale the game properly and not make a LCD TVs usually poor internal scaler muddy up the image and I get better black levels.
I will say the advent of TVs with 120hz is bringing back the level of motion clarity enjoyed by a CRT. It still uses sample and hold but the rate is so fast that it looks great with black frame insertion, but we are still a ways off from that being the norm (2D games benefit from this the most). CRT filters/shaders on an emulator can look pretty good, but again - its all about the motion of 2D graphics getting messed up by LCD sample and hold. Emulated 3D (n64, ps1) games can look pretty nifty with a decent CRT shader since the motion clarity isn’t as important and some bob-deinterlacing can give you a good effect as well (see Bloody Roar 2).
I will also say that the Retrotink 5x and OSSC are great options to get very sharp looking scaling on any pre-HD system, and nice CRT-ish interlace effects on 480i signals. You won’t get the nice CRT motion but at least the graphics are sharp and the devices have extremely low lag.
Getting a Retrotink 5x (or a 2x Pro if you don’t want to RGB mod a console) is probably your best bet if you want to play your real consoles on a newer TV and you don’t want to hunt down a CRT. If you have an LG CX or newer use 120hz with the TVs black frame insertion if you’re using an emulator on your PC and you’ll get some awesome results.