Greg Sandow on classical music for beginners:
So if you want to start listening to classical music, ask yourself what kind of music you already like. Do you like, for instance, passionate music? Then maybe you should start with one of the romantic classical composers, Schubert, Wagner, or Tchaikovsky. Do you like brainy music? Start with Bach.You can read more by clicking here. (Via Musical Assumptions.)
Though if I had to recommend just one classical CD, or in this case a classical CD set, I'd suggest Bach's Goldberg Variations, in two performances by Glenn Gould, as reissued in a Sony package called A Sense of Wonder, which costs little more than a single CD, and gives you a bonus disc on which Gould talks about the piece.
The Goldberg Variations is an astonishing piece. It's written in short sections, each based on the same musical design; you can hear that, or at least sense it, so you can start to learn something about classical music's structure. The performances are astonishing, too, but also very different. By comparing them, you can start to answer one question beginners often ask, which is how performances of the same piece differ from each other. And since Gould tells you (on the bonus disc) which performance he thinks is better, you can develop your independence as a classical music listener, by deciding whether or not you agree with him.
My two-cents on the Goldbergs can be found here.