I hate to break it to you, but the world is different now.
M Rated games are awesome, and here's what i'd do:
Start her off easy. Maybe Pokemon, Mario, stuff like that. If I were a parent there would be no way in hell i'd let my kid play Call of Duty, Bioshock, or some other FPS.
As she gets older, you can start introducing her to more mature games like Metroid, maybe the original Doom.
Then just let her grow, and introduce her to different games in the process.
You don't want to have her dive into a sea of gore, shooting, drugs, sex, and crime.
Believe it or not, that stuff can scare kids. And that's a good way of making her NOT want to play video games.