When it comes to choosing a monitor for your new computer, you'll find that there are a huge variety of options available to you. The best thing for you to do is educate yourself on what's available and match it with your needs and budget.
Most people will opt for a newer LCD monitor vs. the older CRTs. CRTs are pretty cheap nowadays, but they're heavy, bulky, and tend to cause more eye strain than LCDs.
When you're shopping for an LCD, there are a few key characteristics that you should pay attention to when comparing models.
The first, and most obvious, is the size of the screen. This is the size of the viewable screen measured diagonally. A 17" to 19" model will fit most users' needs. However, it's up to you... maybe you'd rather have a 20" widescreen?
Next, make sure that your new display can support the resolution you desire. The higher the number supported, the better. For instance, if you have a 19" monitor with a max resolution of 1024x768, you'll likely be disappointed with its performance (1280x1024 is a much better fit for a 19" model).
Of course, be sure your video card can support this resoltion mode as well. You'll be disappointed if you spend big money on an LCD display that supports several high resolution modes, and then realize that your video card can't drive the monitor to its max potential.
Be sure that you can connect your display to your video card. This seems straightforward, but it's often overlooked. If your video card only has a DVI output, and your LCD display only supports VGA, then you'll need an adapter. Personally, I'd stick with a card and monitor that both use DVI. DVI picture quality is superior to VGA. Higher end cards and monitors may support HDMI (High Definition - HDTV) interfaces.
Look for a display with a high contrast ratio. The higher the ratio, the deeper the "blacks" will be on your pictures. This is critical for displaying vivid graphics and watching movies. A 700:1 ratio will usually give you a great picture.
Compare the refresh rates. The lower the refresh rate, the better. LCD monitors with higher refresh rates may leave ghost images or trails when you're viewing fast action video sequences.
And finally, look for models with a higher viewing angle. The higher the viewing angle, which can range from 90 to 180 degrees, the better. A monitor with a viewing angle of, say, 160 degrees, will allow you to accurately view the screen at 160 degrees from side-to-side.