All good advice so far:
Carmen and
La Boheme are obvious, and good, starting points because they have recognisable "numbers". Personally, I don't much care for Puccini, but he is the best example of the sort of opera that you seem to like now. Check out as well Verdi's
Requiem, which is an opera in all but name & text.
Opera developed away from the "aria" style so try Verdi's
Otello, which is considered by many to be his finest opera and begins the move towards more integrated dramatic music, paving the way for Wagner, who really is the watershed composer.
In the twentieth century, I agree that
Lady Macbeth of Mtsensk District is an accessible and emotional opera, as is
Katya Kabanova by Janacek.
The Turn of the Screw by Britten is a masterpiece, and more attractive than his other operas if you like female voices.
Finally, I'd say that the trick with opera is to
see it: on DVD if necessary, but live for preference. Seeing Wagner's complete Ring cycle on stage was for me a personal milestone event, even though I am not a big Wagner fan, and opera on stage nearly always "sells" a work even if it previously made little sense on disc. Moreover, there's the benefit that once you start paying for opera tickets, headphones no longer seem so expensive!