For color depth, monitors are completely analog, while video cards do their best to provide a wide spectrum of digital color depths, up to 8 bits per color (256 different "shades" of red, blue, and green), giving 16.7 million colors.
Refresh rate, resolution, and color depth are dependent on the monitor, the video card, and the options you select in your operating environment's setup.
I prefer a resolution of 1152 x 864, a color depth of 64,000 colors, and a refresh rate of 70 Hz in Windows 95 on my NEC 17" monitor. Sometimes, I'll switch to 800x600 at 16.7 million colors (true color), and 85 Hz or 1024x768 true color at 75 Hz.
When picking your video card, look to see if it's got a high-speed (220+ MHz) DAC capable of spitting out the high color depths at the high scanning rates - your eyes will thank you.
Things to look for:
Similar to the coating on high-quality camera and binocular lenses, this is identified by its surface that reflects purple light only, not green or yellow or white. You will pay a hefty premium for this "professional" look, perhaps US$ 100 to $ 200.
No doubt this is the major difference between a $ 250 and $ 400 monitor. Popular controls include on-screen (which are quite nice) and a slew of well-labeled buttons under the viewing area. Analog is for sissies.
Those stupid doors that cover buttons on the bottom of the monitor are destined to break. You must resist the urge that these doors protect from dust or hide (unsightly?) buttons. They will do neither when broken.
I've hardly ever needed to use it, but it's a neat party trick. Use it to annoy your friends while playing Tie Fighter or Quake.
Trinitron or flat-square (FS) spherical?
It doesn't really matter very much, but I think the spherical monitors are a little flatter and do not suffer from vertical line distortion. Sony holds the patent on Trinitrons, which are cylindrical.
Energy star ratings and APM are old-hat, but look for this and MPR II ratings for emissions compliance.
Mine has a 85 MHz bandwidth, and NEC is usually behind its lower-priced competitors in this area. You can probably ignore the horizontal frequency if you compare the bandwidth spec and of course, the main monitor buzz-word: vertical refresh rate. My monitor goes up to 100 Hz, but you can probably find 160 Hz (take the NEC XP21 for instance, a 21-incher) monitors now, if only the video card could handle it!
Essentially, higher refresh rates mean more ergonomically-correct, eye-pleasing images. Stay away from ever using a 60 Hz refresh in a fluorescent-lit room, unless your brother runs an eye clinic. 75 Hz is the refresh-rate-of-choice for the author, although I deal with 70 Hz when I run 1152x864.
It's that spec you just can't forget, because the salesmen will be quick to spout it. I like 1024x768 and 1152x864, but 1280x1024 is too small and not offered above 60 Hz for my equipment. Basically, the size of your monitor will dictate what resolution you enjoy. A 15" monitor is better suited for 800x600. It's important to include refresh rates allowed at the monitor's maximum resolution - for instance, why would you ever view 1600x1200 if you must do so at an interlaced 43 Hz? It's unhealthy and not useful without a 19" or larger monitor. So be reasonable when comparing monitors.
I personally think the monitor should be your baby. If you get the right one, it can last 6 years or more (meaning two computer generations) and still be nice. So spend a little extra, get that 17" or 19" monitor with the best features (not the 5-ear old fixed frequency one), and admire it for many years. If you take care of your monitor, it will take care of you. It will outlast your motherboard, it will be the main link (see pointing device for the other one) to the Internet and anything else you do on your computer.
As for video cards, there's a lot of them out there which will work fine. Check out PC Magazine or the equivalent and see which PC has the fastest video card. Get one just like it.
4 MB may not be worth the premium you'll pay over a 2 MB card. If you have a large monitor, get the 4 MB (or more) card, since you'll need it for higher color depths at the resolutions you'll like. Stick with 1 or 2 MB of video card RAM for the 14" monitor guys out there