Glad to hear you're expending your musical horizons! There is just so much great music out there, I always feel bad for people who consciously choose to miss out on some of it. (I have extremely wide and eclectic tastes in music.)
So, to answer your questions:
1. if you want to try out Classical, I think it's best to start with the "Classics" if you will;
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Pachelbel: Canon in D - The ultimate soft and mellow classical song. Romantic and melodious, it has a repetitive theme much like the "hook" in modern music. You most commonly hear it played at weddings as a "processional" song.
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Vivaldi: The Four Seasons - Not a single song like the canon above, but an entire suite of four "Concertos", each one encompassing a season of the year. Each Concerto is intended to emotionally evoke the feeling of that season as experienced by the people living in Renaissance era Italy. Like much of classical music, this one is rather long. I recommend taking it in single-season bites, as even those are quite a bit to digest.
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Wagner: Ride of the Valkryies On a COMPLETELY different emotional note, this is a very well known piece, used in the film "Apocalypse Now". It is actually a small part of a German opera called "Der Ring des Nibelungen" or "Rings of the Nibelungen" or "The Ring Cycle". which is a hugely long and complex opera about German mythology and folklore with a hero's tale that was later echoed in (of all places) Star Wars. Very interesting if you are into that sort of thing.
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Mozart: Eine Kleine Nachtmusik - One of Mozart's most famous compositions, and for all the right reasons. Light, airy and quick with strong repetitive "hook" themes, it's known the world over and has been re-used in more multimedia productions than I could even begin to name.
I think that's good for a start. Obviously there are far more good choices and please don't take my leaving them out as some kind of disapproval of them. This is just what I came up with off the top of my head.
2. As you might have guessed I love classical music (really, music of all kinds.) I spent 8 years growing up playing the violin, and you just don't do that and NOT come away with a solid appreciation of classical music.
Enjoy!
P.S. You should also check out Jazz and Blues music too. I particularly like Ella Fitzgerald (Jazz) and B.B. King (Blues). Do a Youtube search on them for more info.
Hisao: You want to know who I am? I'm the boy with the broken heart.