Mother [who loved it and played it incessantly]

Like mrmichaelwright, I'm not a fan of the phrase "Classical", it really only covers a short period in the history of music, and even then you'll find a split between the modernists and the romantics.

As for starting off, go with the more famous composers to begin with, Mozart, Beethoven, Bach, Mahler, Wagner etc etc, find a period/style that interests you, and go explore.