Video system can not be considered as having any direct influence in PC performance. However in certain applications like AutoCAD, 3d studio, 3D Games, HD Video, features on your graphics hardware can significantly enhance the result obtained from these applications. 

High-end graphics cards come with separate processor, and their own memory to deliver maximum video performance. NVIDIA is one company who makes such high end graphics cards.

This is written for the ordinary PC users who use the PC for simple word processing, spread sheet, Internet browsing, and e-mail etc. For these applications, do not worry much about the graphics hardware. It has almost nil affect on PC performance. What such a user need to see is whether they can configure their display with resolutions like 1024 * 768 and higher in a flicker free mode and that the graphics card has the capacity to do that.

lot of details about the graphics hardware can be found by going the display propperties in the control panel of windows. it would tell you how much memory is available on the card too.

Only if you are planning to use very high resolutions you would need to chose a card with higher memory. Another situation will be like the one where you are using 3D games etc.

Next : Internet performance.