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Your display monitor is not as important as your video card for performance. Laptop displays are slower than the standard Cathode Ray Tube (CRT), but both are much faster than the video cards that drive them. You want a card with enough video RAM (VRAM), sometimes called Windows RAM (WRAM), to hold your entire display at its full color depth. Your video speed will increase with additional video RAM only up to this point. 2 MB is usually enough, but you can get up to 32 MB.
You can get a feel for your graphics performance by noting how quickly and smoothly you can scroll or drag around a window, or flip between different open windows. Some high-performance video cards currently on the market (for example, the 64-bit Matrox MGA Millennium II and Intergraph's Intense3D) are Accelerated Graphics Port (AGP) cards. Some motherboards have a video controller built in, which makes the computer a little cheaper, but also more difficult to upgrade.