Well, it depends on the angle we're going with.
- "Puyo" as the trojan horse for a Madou Monogatari series in all but name: probably a remix of TRY OUT/Memories.
- A Puyo Puyo series starring Arle as the main character: probably a remix of her theme.
- A Puyo Puyo series starring a combination of Arle, Amitie, Ringo and Ally: probably something original, or based on a memorable Quest song.
- A Puyo Puyo series that has no true main character, but an Ensemble Cast (that happens to include the above four): definitely something original.
Also, is the series comical, serious, episodic, continuity based, or something else?
More than anything, I think the answer is too varied. The safest bet would be Arle's theme, an immediately recognizable song to anybody who has ever heard of Puyo Puyo (even Mean Bean Machine has a remix of it in the cast roll).
Actually the concept of a Puyo animated series leads me to think of something I'd prefer: a Puyo comic adaptation. Mostly to get new fans up to speed, partially to see what the comic adaptation would change for some games (in particular, imagine Puyo 7 with Lagnus, Ocean Prince, and maybe if we're insanely lucky Doppel) should SEGA permit it.
Edit: Uh oh, I'm the last post. So I guess here I can now mention that Puyo 1 SEGA Ages has been delayed for better optimization of the online component of the game.