No problem...
First thing is to decide between LCD and CRT...
LCDs are getting better and cheaper all the time and they eliminate the three biggest bugaboos of CRT monitors: focus, convergence and linearity. Since the LCD image is produced by individual triads in fixed locations rather than a scanning beam they can't go out of focus, can't have bad convergence and the linearity is good enough you can actually use a ruler to check the relative sizes of things.
CRTs are faster and when well adjusted they can be as well focused as an LCD (although it is rare to see this in a production model). You won't get the "smearing" effect you sometimes see when things move on cheaper LCDs, which may be an advantage in fast paced games or watching videos. (but LCDs are rapidly catching up!)
Technically the CRT system is about 100 years old. Find an antique radio from the early 1900s with the "magic eye" tuner in it and you've found an early use of CRT technology. Of late I've been making quite the project of getting all my customers switched over to LCD "flatpanel" displays and so far nobody's bitching at me

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Without getting too deeply into how they work...Should you decide on a CRT display there are a number of things you should take into account:
1) Trinitron and Diamondtron CRTs have two lines across them that you can't get rid of and can't hide. These are actually voltage equalization wires, part of the aperature grill they brag about, placed right in the path of the electron beams. Some people just shrug and accept them but others find them extremely annoying. It's bad tech used to cover a bad design and unless there is some overriding factor, I'd suggest you pick a different monitor.
2) Factory adjustment. CRT monitors have a number of factory/repair level adjustments inside. Accurate setting of these can seriously improve display quality. Unfortunately, most factories (esp. those who've transitioned from television sets to monitors) don't take anywhere near enough time on these adjustments. So, you should expect to see highly variable display quality, even between monitors of the same make and model.
3) User adjustment. On CRT monitors, you want a certain minimum set of user adjustments: brightness, contrast, colour balance, h/v sizing and centering, rotation, pincuishion and corner pin. On larger monitors you also want convergence adjustment. (Nothing annoys me more than a crooked, off center image you can't fix.)
4) Case Colour. As I've already explained, black or charcoal monitors appear to provide better focus and brightness. There are designer coloured monitors out there but these will have the effect of skewing your colour perception and should be avoided.
The things that will affect your satisfaction the most are Focus and Convergence. Unfortunately both of these are factory adjustments and can vary over a wide range, even between monitors of the same make and model.
The focus is obvious, nobody wants to look at a blurry image.
Convergence is a bit more complicated. CRT images are formed by scanning electron beams across the screen in rows. As these scan they hit small dots of coloured phosphor on the screen causing them to glow. All colours are produced from combining tiny dots of red, green and blue. Hense there are 3 beams used. For this to work correctly all three beams must be perfectly coordinated so that they land on the same colour "triad" at the same time. To fail to "converge" properly will produce (at minimum) fuzzyness or (at worst) distinctly coloured shadows under objects on your display.
To check convergence you generally need test patterns but, for a quick check, you can always pop up a DOS box and use ALT-ENTER to make it full screen. Do a DIR command and look closely at the displayed text. Are the edges nice and crisp? Are the individual dots clearly visible? Do the white characters have red, green or blue, shadows under them? Basically, anything you see on a DOS screen that isn't a razor sharp white character is a problem. If it's all nice and sharp the odds are the convergence is more or less OK.
If it is at all possible, I suggest you check the actual monitor you will be taking home before you spend your money. If there are problems you don't have to go shipping the thing to China or lugging it back to the store. An interesting side effect of this is that often you can save a few bucks by buying the one on display...
Hope this helps...
--->It ain't better if it don't work<---