*hops on classical train and kills the conductor with a fire hydrant*
Arnold Schoenberg is a brilliant composer, he wrote my favourite song if you haven't already listened to it because I mention it a lot.
John Cage is probably my favourite composer, but he's not always accessible. I would recommend reading his writings and listening to the songs that he discusses as you come upon them. While I love what his music sounds like, I appreciate his writing about the philosophy of his [sic] music more.
John Zorn composes some frantic and haunting classical music.