Luigi's appearance depends entirely on your level time for the first Adventure mode level.
Luigi is a hidden character and needs to be unlocked before you can play as him. As a matter of fact, players accustomed to Mario are likely going to be surprised and perform miserably the first time they play as Luigi.
Though Luigi in SSBM doesn't have his ghost-sucking vaccuum cleaner, he isn't a simple Mario clone either. A hidden character in the original Super Smash Bros., Luigi finally got his own game on GameCube: Luigi's Mansion. When Luigi didn't show in Super Mario 64, Nintendo fans around the world requested a return of the oft-forgotten second Mario brother.