Bowser has captured Peach (for the billionth time...) and takes her to his own new universe, the Golden Universe (roll credits!) where Mario must travel through in order to rescue peach (for the billionth time!)
A Luma pirate called "Capt. Starbeard" is willing to help Mario, taking him around in his Star Galleon, but Mario must collect stars to power the ship and go to the center of the Golden Universe
The iconic plumber has to travel to another universe to save Peach, basic stuff. Mario is the default P1 character.
Luigi: Mario's brother is going into space too, Luigi is the default P2 character.
Captain Toad ditches the backpack and helps Mario in his journey. Capt. Toad is the default P3 character.
A generic blue Toad, default P4 character.
Jerry the Shy-Guy:
You unlock this little guy by beating the mission "Masked little buddy"
Koopa the Quick:
Mario's racing rival can join him after beating all Koopa the Quick missions within 1 minute (per mission, not total)