Since Pit watches the stadium explode, I'd guess he's (one of) the first characters you play as after Mario and Kirby.
It appears that so far we know...
Scene: Mario and Kirby fight, make up, bad guys show up in Meta-Knight's ship, Zelda and Peach show up.
Level: Mario (and possibly Kirby, Zelda, and Peach) fights the little purple bad guys.
Scene: Ancient Minister and ROBs set bomb. Mario gets KOed out of stadium by Petey Piranha, who then puts Zelda and Peach in cages.
Level: Kirby fights Petey Piranha, releasing either Zelda OR Peach.
Scene: ??? Who knows? The Stadium ends up blowing up/getting transported to Subspace.
Scene: Pit see Stadium explode, sets out on own adventure.
Level: Platforming with Pit (???)
Who knows how this will really work, though. The fact that you choose who to save with Kirby suggests to me that at the very least, you'll be able to play some levels with different characters. But maybe you can play almost any character on almost any level, depending on your choices and actions.
"[Our former customers] are unable to find software which they WANT to play."
"The way to solve this problem lies in how to communicate what kind of games [they CAN play]."
Satoru Iwata, Nintendo President. Only slightly paraphrased.