I would go with the St. Matthew's Passion. If I could only salvage one track from Western culture, it might be "Aus Liebe will mein Heiland sterben," the soprano aria that is the capstone of the piece. Pictured is the best recording I know of it. I would say it's more intimate than the B Minor Mass, more focused on personal emotional responses to the passion story. Bonus that I would get three cd's worth on my island.
If I got to take 10 songs, like on the BBC show, then definitely some Mozart. Piano concerto No. 23, especially the second movement. Or the Magic Flute: I would call my bloodied volleyball Papageno. And Schubert's D 960 piano sonata would be a much-needed consolation on cold starry nights.
Flying Dutchman would be my ironic, seafaring choice -- though actually I don't know the opera.
Some early Elvis Costello for some rockin' snark, like when you've just cracked open a coconut you've been working on all morning.