Hi,
Lots of the information you are seeking has been discussed at length in the foums. It's worth doing a search through the archives on a few keywords.
See my and other contributions to this thread for a general overview;
http://www.avforums.com/forums/showthread.php?threadid=44705&referrerid=12726
regarding CRT/LCD differences, there's tons of info. Here's a quickie (all generalisations, there are notable and honourable exceptions to all points);
CRT will give you a better (more film-like) image with no pixelation
LCD will give you a brighter picture
LCDs are small and portable, CRTs are big and heavy
CRTs requires a fair degree of setting up and some onging maintenance/calibration
CRTs give better/deeper blacks, LCDs can look grey
CRTs dont have bulbs to blow
CRT tubes wear out over time and are expensive to replace
CRTs require some form of scaling to work at their best
CRTs support multiple resolutions & refresh rates, LCDs tend to offer best performance at a number of fixed points.
New CRTs are very expensive
Used CRTs are very cost effctive!
Others will probably offer advice on brands but Sony, barco and NEC seem to be the most popular on here. Very important to get a Graphics or data model, not Video.
Depending on tube size (7,8 or 9 inch) and environmental conditions, picture size will avry. With a CRT, the bigger the screen, the less bright the image becomes. Screen material can compensate for this somewhat. I'm running a Sony 1271 on a 9' wide 16:9 screen in a totally light-controlled room with excellent results.
Distance will depend directly on screen size and varies from projector to projector. As an example, the front of my CRT is sited just over 9' from the screen. (see pictures on my site, linked below)
In terms of your budget, I'm sure you can pick up a decent CRT for that. bear in mind, however, you will need a screen, scaler or HTPC (home theater PC), sound system etc.
Pay particular attention to posts by Roland or Gordon on these foums. They dedicate a huge amount of time here and will not put you wrong.
Good luck with it
Peter