If you are thinking about multiple monitors, then you need a graphics card that will support it. Two screens should be fine for eight games (four each). You can use "Extend Display" from "Display Settings." If you want more monitors, expect to spend $500 on a graphics card like AMD's Eyefinity.
Even using a single monitor, a graphics card is probably the most important part of your computer. Don't get the cheap one. Spend at least $100 on a good graphics card, and make sure it can easily support two screens.
I assume you will be running a HUD while playing. If so, you'll want a good processor and decent memory. You don't need gaming speed, but a better speed will mean longer before you need to upgrade. Solid state hard drives are nice.
I think any good (upgradable) desktop with two monitors will work fine. The problem with laptops is their limits on upgrades. Even the best computer could be outdated in five years. A desktop allows you to easily upgrade or replace parts.
And again, graphics card is probably the most important upgrade.