The video card is probably the second most important component inside the computer. Make sure that the card connectors match those on the motherboard, i.e. if the motherboard has VESA slots, you want a VESA video card, PCI, PCI. Only get an EISA or ISA video card if your motherboard doesn't have VESA or PCI. This will give you maximum speed. The newest thing is AGP, Accelerated Graphics Port. To be able to use an AGP video card, you need to have an available AGP slot and a motherboard can only have one.

Something else that is an interesting novelty with Windows 98 and Windows NT 5.0 is the capability to connect multiple monitors (up to 8 with Windows 98) to the same computer. My first thought was: "Who would want to do that?", until I understood that you can drag windows from one screen to another using a mouse and have multiple resolutions on different monitors at the same time. This capability works well when you're constantly switching between applications.  One caution is that the multiple monitor configuration requires multiple video cards.  Many motherboards won't recognize an AGP video card as the primary monitor.  While a cheap video card works fine on the second monitor, you don't want the cheap card running your primary monitor and your AGP card running the secondary monitor.

The amount of memory you need on the video card depends on the resolution you plan on using and the number of colors. This little table shows the relationship between storage and number of colors:

The following table shows the relationships between resolution, memory, colors, and monitor size:

You need to consider the vertical refresh rate. Normally you want a refresh rate of 70 MHZ or better.  Less than this was cause noticeable flickering.  The higher the resolution is, the slower the refresh rate will be, so you need to decide what resolution you want to use most of the time and buy accordingly.  The video card should have a higher refresh rate than the monitor.  Also consider the type of video memory. SRAM is faster than EDO and EDO is faster than standard.  For video cards I recommend Diamond or Matrox. Other good cards are made by STB, ATI, and Number Nine.

Monitor

Definitely get one that's .28 dot pitch or less. 17" monitors are cheap enough now that I wouldn't consider anything less. The larger monitor you get, the more data you can see on the screen or the bigger the characters are going to be. Refresh rate is as important on monitors as it is on video cards.  You want to make sure that the monitor you purchase has at least a 70 MHZ refresh rate at the highest resolution you plan to use.  The size of the monitor also needs to be factored into this decision, since some resolutions aren't practical on smaller monitors, e.g. 1024x768 on a 14" monitor.  Other factors to consider are sharpness, brightness, stableness, and color resolution. I've had very good luck with Viewsonic, Sony, and NEC.

Right now I'd stay away from the flat LCD monitors.  They look nice, but they're expensive, and we don't know how long they're going to last.  If the price was comparable to a CRT monitor, then I'd consider one.