If you've decided to get a new CRT then it should have a sufficiently high refresh rate. This refers to how often the screen is redrawn per second. With low refresh rates you can get screen flicker and eye strain. Aim for a rate of 75 Hz for a monitor up to 17 inches in size and 85 Hz for any larger monitor. LCDs are basically flicker free so refresh rates aren't important.
Another consideration for CRTs is dot pitch. This is the distance in millimeters between phosphors of the same colour. The smaller the dot pitch, the sharper the image. Opt for a dot pitch of 0.26 mm or smaller. You can measure dot pitch both horizontally and vertically, but monitor specs usually quote horizontal dot pitch. Occasionally, the dot pitch is measured diagonally. By multiplying diagonal dot pitch by 0.866, you can calculate horizontal dot pitch.
One of the main disadvantages of LCDs when compared to CRTs is their limited viewing angle. When viewing a LCD straight on it looks fine. But the screen will appear washed-out if you move your head over to the side and look at it from an extreme angle. Low-end LCDs can have viewing angles of only 100 degrees which won't give everyone crowded round your desk a clear view. For a standard 15 inch LCD try to get a 140 degree viewing angle. Up that by 20-40 degrees when shopping for an 18 inch LCD.
The brightness of LCD monitors is another important factor. LCD monitors have several backlights that provide illumination. Brightness is measured in units called nits. The majority of LCDs produce 150-200 nits which is fine for most users. The backlights in a LCD are good for 10 to 50 thousand hours of operation.
Since they're fairly fragile and more likely to break, backlights usually come with only a one year warranty. This warranty is separate from the one for the screen so you might want to extend the backlight warranty to match the duration of your screen warranty.
LCDs can provide a range of options for positioning a display. The common way to view a screen is landscape mode (longer than wide). Some LCDs let you pivot the screen 90 degrees so you can view it in portrait mode (taller than wide) which is great if you're growing tired of scrolling so often. You should also check out whether the screen can both tilt and swivel. Easy adjustment is important if you'll be doing presentations. You can even mount some LCDs on the wall like a picture.