Well although most people are suggesting the older games, why not start her with whatever's new in 5 or 6 years? Unless its still as violent as LoS I mean. I'm sure most of us started playing any game that was new at the time, then out of curiosity saught out the older games.
I know that not everyone is the same, but was young I started with a Sega Genesis which was still new at the time, and I grew to love games pretty naturally. Even though I grew up with modern consoles, I still went back to play the classics to better understand the franchises I loved.
Perhaps it will be the same for your daughter, just wait and see as she gets older.