Again, it depends on what you plan to do with your computer. Bear in mind, what you intend to do and what you actually end up doing may be drastically different. It's good to give yourself some elbow room, unless you're on a tight budget. As far as branding goes, Sony is great, Apple is superb for graphics because of their accurate color-matching capabilities and bright screens, and I've also heard good things about Radius and ViewSonic. If you're into graphics, publishing, or Web design, I'd advise against trying to get away with using a cheap monitor, such as an eMachines or Compaq. Sub par color-matching, contrast, sharpness and controls will bite you in the ass later.

15"
Adequate for general needs, but graphics people will feel stifled.

17"
Very nice. Great for graphics, Web designing, desktop publishing, video editing, etc.

19-21"
Same as above, but more so.

LCD Monitors offer a nice alternative to CRTs (Cathode-Ray Tubes) in the way of flatter screens, smaller profile on the desktop, and much lighter weight. Some caveats are the price, which can be a thousand bucks for a 15 incher, and their narrow viewing angle, which means you have to be looking nearly straight at them, else they look washed out.

"Shared RAM" -- Beware
I've read that some computer companies try to cut cost by using part of the system's memory for video, rather than having seperate video RAM (VRAM). Since this takes RAM from the system, and forces the video to use regular RAM, rather than faster video memory, the performance of both will be affected. So, scan the fine print, and ask how much VRAM a model has: If they mention "shared RAM," look out.