Personally, I think a great way to start is with Mozart, especially The Magic Flute. Der Fledermaus (Johann Strauss who in most ways I despise) is also really fun and very accessible.
I am not an opera fan...but...
Disclaimer---I am not much of an opera fan. However,I get the occasional jones for an opera fix or at least the feeling that I should be trying to like it. (Especially when I'm in my "godfather" mode) I recently bought a CD entitled "Simply the Best Night at the Opera. This one satisfies my needs. It is great.