The Planets - Gustav Holst, my personal favorite piece of work. Youd better have a system capable of good dynamics though, I learned the hard way.
Beethoven's 9th - Ode to Joy. Need I say more?
Beethoven - Moonlight Sonata - the most beautiful, emotional piece of piano music ever
Gerschwin - Rhapsody in Blue - modern classical, it has a somewhat jazzy sound with more use of woodwinds
Bach - Tocatta and Fugue - if you like the organ, you probaly like this, you know the tune, also Fantasia is good, and his 3rd Brandenburg concerto is quite nice
Pachabel's canon is proably one of the most copied pieces of music, quite deservingly so.
Vivaldi's four seasons is beautiful, and while it might be a bit 'lite' for some people, you have to sit back an experience it as a whole, it also helps to imagine what is going on as it goes on, or it will probably drag.
Quite frankly there is no best classical performance, but so much of it is so good that you just need to get something of a type you like, and you will probably like it. If you are just starting though, I would reccomend staying away from Part, he, and some others have a much more abstract style that is harder to get used to.