Well with CRTs its alot easier to pick one. Most are pretty good, so I wouldn't worry about picking one.
For CRT's, look for the viewable screen size (usually listed) or bring a ruler.
Then the dot pitch - smaller is better. Aim for less than .25, go for a .20 or lower.
LCD's aren't bad. I'd say take a look at them if you can. You can probably get a decent one. Remember that the refresh rate is somewhat important.
Hopefully they'll let you play a game or a movie on the LCD, which should let you detect artifacts, ghosting, etc.
Remember that specs are important, but most important is how you like it. If you like one and can't tell any ghosting, etc, don't write it off just because it has a 20ms refresh. If you can't tell, then you won't be able to tell w/ one w/ a smaller refresh. (In theory, but other factors contribute to that too).
For $250, an LCD, you might haev to settle for analog (15-pin) input. But hey, if you don't have DVI to begin with, who cares?
Here's an envision widescreen for 250:
http://www.circuitcity.com/ssm/Envision-19-LCD-Monitor-H191W-/sem/rpsm/oid/147648/catOid/-12965/rpem/ccd/productDetail.do
acer for 270
http://www.circuitcity.com/ssm/Acer-Monitor-AL1916S-/sem/rpsm/oid/138184/catOid/-12965/rpem/ccd/productDetail.do
check out newegg, they've got benq, viewsonics, hyundais for under 250ish.
Also remember that LCD measurements are real. 19" = 19"viewable.
CRT's don't follow that rule.