Hmmm. Let's see. The three series I play the most are:
1) Mega Man - I suck at those games so they can last me a good loooong time. And they're usually get up and go, so that's good for replays.
2) Legend of Zelda - Games can last a while. Good puzzles and action/adventure gameplay which is swell. A nice variety of exploration and action.
3) Final Fantasy - Not the most immersive gameplay-wise, but they take forever to beat so that's a pro for this choice.

So my answer is... draw from a hat.