Note: I use the term LCD in a generic manner here to refer to all types of flat-screen displays, regardless of the specific type.
LCDs have the following advantages over CRTs:
1) they use a lot less power than a CRT.
2) a 17" LCD gives you 17" of actual display. A 17" CRT gives approximantely 15.6" of viewable disply. The discrepancy is due to the way CRTs are built and the fact that that the outer edges of a CRT distort so much that they are essentially unusable for viewing. A 17" LCD has the same viewable screen area as a 19" CRT monitor.
3) LCDs are much more compact than CRTs. The shallow front to back depth means much less space used on the desk. They are also much lighter than CRTs.
4)CRT is considered to be obsolete technology. It is getting difficult to find brand new CRT monitors. You may not have much of a choice here.
Main disadvantages of LCDs vs CRTs are:
1) All LCDs operate at a specific native resolution. Usually, this is a pretty high setting. 15" LCDs usually work at 1024 x 768, 17" & 19" usually run at 1280 x 1024 (or higher). This means that your text and icons and many other items are pretty small. This may not be an issue if you are young and have good vision, but if your eyesight is less than perfect, there will be a problem. If you are older (over 40) this will definitely be a concern. The weakness of LCDs is that if you don't run them at the native resolution, image quality deteriorates noticabley very fast. Text gets fuzzy when the font is large and illegible when small. All other screen elements also degrade. Sometimes, overall performance can also degrade. Note that on many LCDs, text in particular is rendered poorly even at the native resolution. This can lead to vision problems down the road. CRTs produce sharp and clear images regardless of which resolution they run at, with no loss of performance.
2) LCDs really don't like colour depth settings below 32-bit. This is not normally an issue, except for one significant segment of software. Specifically, kids software. It is amazing how much of the current product will not run in anything other than 256 colour mode. The reason is that most of the software for kids was originally produced to run under Windows 3.x. The manufacturers have repurposed the software to run under more current versions of Windows, but have not recoded the video portion of the application. This may not be a concern for you at this time, but it likely will be in the future. CRTs work just fine at all colour depths, including monochrome.
3) CRTs have refresh rates, LCDs have response times. These relate to how quickly the image on the screen is redrawn, and have an impact on image clarity and eyestrain. Until fairly recently, LCDs with response times of less than 10 milliseconds were not that common and quite expensive. This is an issue when moving images are displayed and when scrolling through text quickly. Moving images tend to be blurred, and have "tails". Scrolling text tends to be blurry, especially in File Manager, which slows down searches. Even the LCDs with response time below 10 ms don't perfrom as well as CRTs.
4) LCDs are limited in the legible viewing angle at which the contents of the display are clear. This why LCD specs include horizontal and vertical viewing angle - the numbers tell you at which point you can no longer see the image on the screen clearly. CRTs don't have this limitation.
5) LCDs do not work well under very bright lighting eg sunlight. See digital camers for simple example.
6) Lose a few cells and the entire screen needs to be replaced. The number of dead cells relative to the total number is surprisingly small.
For an interesting perspective, you may wish to compare the price difference between LCD Computer monitors and full-on televisions. Where I live Future Shop is charging $220 - $400 for 19" LCD monitors vs $600 for 19" LCD televisions. There's a very good reason that LCD TV's of the same size are significantly more expensive than computer LCD monitors. If you are a serious gamer, then getting an LCD monitor would be a very serious error. For most applications, LCD is perfectly fine, as long as you are aware of the issues and can live with the limitations of LCDs. Otherwise, get a good 19 or 21 inch CRT.
You should also search THG site - they have a number of descriptive articles and reviews that would help.
Hope this helps.