Congratulations on seeing your first Opera. Mine was Marriage of Figaro when I was in High School. I am now a season ticket holder at the Minnesota Opera, who did a lovely Butterfly two years ago. I don't ever need to see it again, it was so good. I see Grapes of Wrath in two weeks, and will be in NYC for the Met's Trittico in April.
Forget all the stuff about Miss Saigon and pursue some of the other operas. You can skip the Wagner, although do listen to Anna Russell talk about them. It's really funny when she says "I'm not making this up, you know." You may want to see the Bergman film of The Magic Flute, which is lovely, or Zefferelli's gorgeous film of La Traviata.
If you ever get to see an opera at the Met, don't miss the chance, because no one can do spectacle onstage like they do. Try to see their Manon or their Dialogues of the Carmelites, because those are magnificent. The 2005 staging of A Masked Ball was incredible, too.
You never start out to be an Opera fan, it just overtakes you and you can't help it. You become obsessed with it, because as great as musical theatre is, Opera will always do it better. I have been a musical theatre fan since I was in sixth grade, and I'm now middle-aged, but I am passionate about the Opera!!
NYC Visitor and Broadway Fan