A little late to this thread, but anyway --
All the above recommendations (good ones) come from the classical, romantic or modern periods, which are the areas first explored by new classical music listeners. After you get acclimated, consider dipping your toe into the baroque and renaissance periods, where vocal music is more common. From the baroque, Purcell's "Dido's Lament" from his short opera Dido and Aneas. From the renaissance, the madrigals of Carlo Gesualdo, whose dark and haunting life is reflected in his music.
