If you don't mind stepping away from the light weights, you might as well start with Doktor Faustus, by Thomas Mann, which in my opinion defines the genre.
Some other nice reads are The Piano Shop in the Left Bank, The Spanish Bow, and Hidden Melodies.
Not precisely on music, but with loads of music references in it, you should not miss Hermann Hesse's the Glass Bead Game.
I find things like "The Soloist" and "Shine" to be intolerably lame. "The Chopin Manuscript" is just criminal (although I must confess it was a fun read).
Read lots. It is good for musicians.