My answer to Joe is to listen to as wide a range of classical music as possible, both with respect to the type and to the historical period of the music. When you find something that you like, or a composer whose works generally please you, then listen to friends who like the same general area. And if you're currently into music that carries a good tune, that's fine because in one way or another that's where we all start. There's no need to be apologetic about liking Elgar's Pomp & Circumstance No.1 or the choral movement of Beethoven's Symphony 9.
You'll possibly find your musical tastes changing with time too; maybe several times over. When I started listening to opera I liked tuneful operas such as Rigoletto, Trovatore, Traviata, La Boheme etc. Then I got into Wagner and Strauss (R.) and temporarily ignored these "immature" works for a decade or so. Now I've learned to appreciate both, and to take in more modern composers such as Janacek, Britten and Berg as well. I've never been keen on anything by Mozart or his contemporaries, but if you find that your explorations take you in that direction I'd be the last to try and dissuade you.
Half my classical friends abhor my abiding interest in Mahler, and the other half can't get enough. It is interesting that there are more practising musicians in the former camp than the latter, but my preferences are mine alone. There was a time when orchestras would not play Mahler for fear of loosing their audience - it would seem that now you have to include Mahler to get an audience for a major symphony orchestra.
As to performers, you might find yourself starting off with Andrea Bocelli, Vanessa-Mae, and Charlotte Church, and you might find that this arouses derision in some circles. Later you might find yourself preferring Jussi Bjorling, Nigel Kennedy and Renee Fleming for example. But so long as you view your original preferences as a personal jumping-off point you can ride this out. There is no right or wrong way to approach classical music, and no right or wrong composers or performers to consider. Reading some of the other contributions to this thread might give the opposite impression, and the whiff of dogmatism contained therein might be intimidating - note the stick I took for an adverse comment - but following your own nose will give you a fascinating journey. There will be some false starts and some unproductive byways, but that's life. And if you eventually find yourself throwing in the whole classical bag for heavy-metal rock (whatever that is, but my kids like it) then that is just fine too. The exploration is the adventure.
