My comments are based on my own limited experience with opera. I never cared much for opera. I did not have the patience to sit listening with libretto in hand trying to follow the action, unable to visualize what was going on. And frankly, the brief "cliff notes" summaries of most operas I read about just didn't interest me.
But during vacation a few years ago, I wanted to go to the symphony, and ithe only thing available was a staged performance of Stravinsky's Le Rossignol by the San Francisco Symphony. I was fascinated. The overall effect of music, dance and vocals (with running translation of the libretto) was interesting, and the "fantasy" story line was much more to my liking than the traditional romances I had looked up.
I was disappointed to discover that the only video (at that time) of Le Rossignol was a mostly animated thing, which was not nearly as interesting to me as the San Francisco Symphony's staged production. But I love the music of Rimsky-Korsakov and enjoy the music from his various suites drawn from operas. And when I looked up summaries of those, I was intrigued.
So I ordered DVDs of Mlada and Sadko and The Golden Cockerel. These were splendid! The combination of fantasy, spectacular visual staging, great music, singing and dance, with English subtitles, was perfect.
Then I decided to try other composers. An obvious, natural choice was Mozart's Die Zauberflöte. Another happy hit, and there are quite a number of videos of this to choose from.
Of course, the greatest of the "fantasy" operas is the Wagner Ring cycle. I had always disliked this stuff on CD/LP. Bellowing Brunhildas, meandering music. Blech! I cannot say that I love the Ring operas, but I gained much better appreciation for them when I could actually see people and sets and follow the "action" in subtitles. I was also less enchanted with Debussy's Pelléas and Mélisande.
I've also begun going to the opera on occasion. There's really nothing going on where I live, but when I travel, I always look for concerts to attend. So, in the last year I have seen Madam Butterfly at the Metropolitan Opera in NY and Rossini's La Cenerentola (Cinderella), and this fall will see Aida in NY.
This is all a long-winded way of making a couple of points. As someone new to opera, and a rather skeptical initiate at that, this is what worked for me.
1. Seeing opera makes all the difference. As John also noted, the visual of video or attending live performances was the key for me. I still cannot sit and listen to opera on the radio or my stereo. And a good video (to me) is an excellent first introduction to an opera, because I can stop, back up, pause, watch the documentary features, etc.
2. Stories are important. Opera is theater. If the story being played out is uninteresting, I feel like I'm wasting time and money sitting there watching it. I like fantasy stories. And personally, I like it when dance is integrated into the opera. That was what grabbed me with Le Rossignol, and one of the aspects of Rimsky-Korsakov's operas that keep me coming back to them.
3. Production makes a difference. I don't care for a lot of the modern, spartan staging with political contexts, etc. In other words, I want to see the traditional staging that fits the story.
Well, okay, that's my story so far. Since I love Russian music, the next operas on my list are Tchaikovsky's.
I hope you find your own successful path into opera.