Video adapters have memory as one of their components. The more memory on the video card, the faster response you're going to get as the screen redraws. You'll pay for it though. For many applications today, a video adapter with 1 or 2 Mb of memory should be sufficient. If you plan on communicating with the outside world, corresponding via email, or accessing the Internet, you must have a modem.
Modems come in a variety of speeds, with of course the bottom line being, the faster the better.
Another feature of modems to consider is if you want the modem to be external or internal. In terms of functionality, there isn't a difference. Many people mistakenly believe that when they request a CD ROM drive, they will automatically get all of the above. If you want all of the above, you'll need a multimedia kit. PCs that include MMX in their names do not require a sound card, but you will need the CD ROM drive.