Challenges and Changes
Why would I choose "Für Elise" to play on a drifting alien starship? For contrast. It's unexpected. It sends a signal contrary to my description of the ship, and that dissonance can be unsettling. If the ship is thought to be teeming with deadly aliens, that contrast can even be kind of spooky or surreal. That puts the characters, and hopefully the players, on their guard. (Or, in the case of Martin O'Donnell and Michael Salvatori's elegant Halo soundtracks, that detachment can create a sense of epic ethereality.)
If it's source music, it also suggests that somewhere on the ship there's a working device actually playing the music, which creates the illusion of a space bigger than what's right in front of the characters and conjures a little mystery: Why is this music playing? When the characters find the futuristic device that's playing the music, hopefully soon, they can turn it off. In which case I, the GM, can turn it off, too. That creates a fun dynamic whereby the characters' actions affect the play environment, changing the atmosphere for both the characters and their players. Your players might not hear "Für Elise" the same way again, now that they associate it with a haunted spaceship.
The music you deploy during play clues the players in to the kind of atmosphere you're trying to create. Conflicting atmospheres - like the collision of a beautiful classic piece with a deadly alien environment - are uneasy, just like you want your interstellar boarding party to be.
Music can influence the players as an audience at the same time that it informs them as actors in the game. It shows what sort of mood you're trying to conjure up and contributes to the atmosphere of the scene - sometimes only subtly - in a way that your description of the game world alone might not. It carries some of the weight for you as the gamemaster and storyteller.
Ultimately, what works for your players is what matters. The only audience you have to please is the one at the game table with you. So build your musical repertoire with your players in mind, add in a few tracks to challenge their expectations, coax their emotions, and get ready to play.