You have awoken the monster avi0903! Never mention you want to know more about classical music arround me unless you mean it.
I wasn't a musicology (music history) major for nothing.
You said you like musicals - so for opera I'd tell you to start with the light stuff - even things like Phantom and Les Mis can be a starting place, Gilbert and Sulivan is always fun (you know - "I am the very model of a modern major general") and in English. Mozart has some comic operas that are quite accessible - The Magic Flute is always fun, and while I always prefer the original language, a translation can be helpful for when you're first getting your feet wet. I honestly find that Opera doesn't record well so if you get a chance go to a live performance - college music departments often have much cheaper tickets and quite good talent. I'm also a big fan of Bizet - if you like to hear bits and pieces you recognize Carmen is a good bet. I would definately suggest staying away from Wagner at first - that'd be like...like loosing your virginity with a porn star. (I don't even like Wagner - though I have a feeling metalheads and other loud music fans might if you gave him a chance)
As for instrumentals - for fans of lighter, friendlier, more cheerful music - my all time favorite is Chopin, but Haydn and Mozart are also great and easy to find. I love Chopin's nocturnes especialy. Boccherini is another happy soul - but a bit more obscure.
For you darker, brooding, louder, sorts - you can't beat Beethoven. Liszt or some of the more (relatively speaking anyway) modern guys like Stravinsky (he started a riot in Paris in 1913 with one of his ballets - its the "dinosaur piece" from Fantasia) - would also probably be good.
Now for jazz which I know alot less about - I'd say for a place to start - get some Billie Holiday and some Louis Armstrong - you can't go wrong with either of them. If you are really interested Ken Burns made a fantastic documentary on the history of Jazz. Super interesting and also a good way to find out what kind of jazz you like or don't like and who does it.