There are a lot of variables at play here, including especially personal preference, but I think a CRT generally looks a lot better than an LCD. And allows you to record the screen and get that classic analog look that you will never get from an LCD.
Maybe think of the CRT phosphor array like film grain, just a little bit of added noise that helps make the image look less plastic, more warm and organic.
That being said, 9" is maybe too small? A 14" PVM isn’t going to be much, if any, deeper (which I personally find to be the biggest issue, space-wise, with CRTs), but will provide much more viewing area.
But, if cost is an issue, I’d suggest just looking for a non-professional CRT, at least at first. You used to be able to get PVMs for next to nothing, but the retro gaming scene has ruined all of that. But, depending on where you are, you may still be able to find consumer CRTs for next to nothing (I bought a flat-screen 14" Trinitron off Craigslist for $10). They won’t have all the same controls, but Sony consumer-grade Trinitrons are still pretty darn good. And indeed, depending on your style, an even more junky TV (because Trinitrons themselves have a specific look) may be better still.