First Person Shooters
are any game where you take the role of a person, and go around shooting people.

Simulations
are games where something is "simulated", duh.

Driving Games
are games where you drive something, duh (again).

Real Time Strategey
these are my favorites, they are mostly 2D, birds eye view games, where you build units and march them into battle.

Sports Games
are probably my least favorite type of games, as you might have guessed they include all the games where you play a sport.

PS2
As a "true" gamer, I despise all those who claim to be gamers simply because they have a console system. And while you can't be a gamer without a PC, there is no harm in having a PS2 for those long months when your game's release date is pushed back.