The most important factors involved in picking a monitor include:

Monitor Type, Size and Viewable Area
Maximum Resolution Settings
Monitor Refresh Rate
Dot Pitch (or stripe pitch)

Recommendations: 17" monitor minimum (16" viewable size), 75 Hz or higher refresh rate, 0.26 mm dot pitch or less, and capable of at least a 800x600 resolution.

Monitor Types and Sizes

There are two main styles of monitors: the standard CRT (like a small television) or a Flat Panel / LCD monitor (shown in the image above).

CRT Monitors - One of the most commonly used technologies for computer monitors, CRT (Cathode Ray Tube) is a technology much like what you will find on most TV's. CRT monitors are affordable, but they are rather bulky and heavy.

Flat Panel / LCD - LCD or Liquid Crystal Display monitors are similar to what is found on portable computers. LCD monitors generally display much sharper of an image, and they are both lighter and more space efficient. However, they are much more expensive than CRT.
Monitors also come in various sizes, which are generally 15", 17", 19" and 21".

Beyond the actual overall physical size of the monitor, you need to check out it's viewable size. The viewable size (measured diagonally) is the exact size of the monitor's viewable glass screen and not the complete monitor.

This is important because it determines how much area you will actually view when using the monitor.

Dot Pitch (or Stripe Pitch)

A monitor's dot pitch is a measurement that defines the amount of space (in millimeters) that separates two adjacent pixels that are the same color. The smaller the dot pitch the sharper the image, For example, a 0.25 mm dot pitch monitor provides a sharper image than a 0.27 mm.

Similar to dot pitch, stripe pitch is a measurement used specifically with Trinitron or Diamondtron monitors and is a measurement (in millimeters) that separates two like-colored stripes.

Like dot pitch, the lower the stripe pitch the higher the display quality of the monitor.

Monitor Resolution & Refresh Rates
The resolution of a monitor is the amount of pixels that it can display horizontally and vertically. For example, 800 x 600 means the display will be 800 pixels wide and 600 pixels high. Standard monitor display is 72 pixels per inch.

The following is a listing of suggested resolution limits based upon monitor size.

15" Monitors - Best at 640x480 or 800x600

17" Monitors - Best at 800x600 or 1024x76

19" Monitors and up - Best at 1024x768 or 1280x1024

The refresh rate is a measurement of the number of times per second the screen is redrawn. This measurement is measured in hertz and it is recommended that a monitor have at least a refresh rate of 75 MHz at the resolution you wish to run at.