I actually thought Brighton and Twila could've fit into a Paper Mario game or something.
All the plots, for convenience's sake:
MP1: Mario throws a party, but they get into an argument over who's the "Superstar", which I assume means "best character" in non-self aware terms. They decide to go do good deeds by collecting Stars in the worlds beyond the Warp Pipe. Bowser is also there. When you save up 100 Stars, Bowser appears in the village and robs the bank, so you have to go to the final world to get the stars back and repair the Eternal Star. The end of the game reveals that the characters reached an agreement and decided that nobody is better than another.
MP2: The plot is about how "Mario Land" was built by Mario and everyone, but they argued that it should have a different name. Bowser decides to attack the place, so Toad suggests that whoever stops him gets to name the Land. It's later revealed that Mario Land is a theme park and that the plot was an animatronics show. Basically, it's a parody of the first game.
MP3: The Millenium Star, which is born every 1000 years, crash lands in front of Peach's Castle, so they (once again) argue over who gets to keep it, as whoever has it becomes the Superstar of the Universe. They opt to open up a toy chest and play a round of "Mario Party" for it. Then the Millenium Star comes to life and teleports everyone inside the toy chest (which looks a lot like Paper Mario) and tells them that they must beat his challenge to in order to become the Superstar.
The campaign mode has little cutscenes showing each round where you earn a Star Stamp for beating a board. Wario has the Wit stamp, Yoshi has the Kindness stamp, DK has the Strength stamp, Peach has the Love stamp, and Mario has the Courage stamp. Luigi is actually the default character, and if you pick any of the others, he takes their place, thus making him the canonical main character of MP3. Every time you win a round, Bowser always tries to steal your stamp, and fails in the most comically stupid way possible.
Then you beat Daisy for the Beauty stamp (the MS almost declares her winner immediately), and this time Bowser decides to ambush you for the last stamp, the Mischief stamp. Then you find that Waluigi stole it. Bowser is mad at being upstaged, and promptly loses a fist fight against Waluigi. Then you have to beat the final board (which is an island formerly owned by Luigi, now taken over by Waluigi), and eventually challenge the Millenium Star himself in one last mini-game.
When you win, he reveals that he's a fake and runs off, but the real MS turns out to actually be hiding inside Tumble's (the magical die guy) die head and christens you the Superstar of the Universe. The End.
For the record, MP3 is my personal favorite, with MP2 running second.
