In an unusual deviation from protocol, I’ll attempt to answer the original question before going off on far more interesting (to me) digressions.
No Puccini suggestions since he is a personal blind spot; I quite like Tosca since the best bits are ripped off from Mussorgsky. Verdi is much safer ground. Rigoletto and Il Trovatore are the obvious follow-ups to La Traviata followed, after a suitable period of singing the tunes whilst you whisk up a quick spaghetti carbonara, by Otello and Falstaff. Other random thoughts: Handel: Guillo Cesare, Mozart: Don Giovanni, Die Zauberflöte and Figaro; Rossini: Figaro - the prequel (Barber of Seville). If I were to recommend any Wagner it would probably be Die Walkure, but I wont. No need to start with Rheingold since Wotan conveniently reminds us of the story so far in Act 2!
A large part of the perceived silliness stems from my inability to understand the vocals (regardless of the language), but once I have a closer look at the libretto it gets better.
I can only fifth the recommendation to see opera live. It is much better still when you see a well-directed bunch of singing actors telling the story.
Munich opera is world-class but your country is also blessed with numerous very decent smaller houses which don’t attract the starriest casts but will have a repertory company used to rehearsing and singing together which has many advantages in putting on a convincing show. These also have the advantage of reasonable ticket prices and smaller theatres so singers don't have to strain to fill the space. I went to see The Ring in Weimar a few years ago and in many ways it was the most enjoyable of the 6 different cycles I've seen. This from an opera company of a town the size of Chesterfield or Shrewsbury.
Films/DVDs should be the answer if you don’t fancy or can’t make it to the real thing. I’ve never quite fully bought into opera on DVD though. I think I am too used to film being ‘realistic’ whereas opera is obviously highly artificial.
I can strongly recommend the Kaufmann CD palpnorte mentions. I saw him at the Festival Hall the other week. Fabulous. It may be heretical, but the Verdi items were even more convincing than the Wagner.
Kaufmann has recorded Sigmund already, unfortunately for <spit> Gergiev. What’s worse, it gets excellent reviews. I’m not sure if he wants to play Siegfried though.
Tickets for La Boheme tomorrow from £19 at ENO, - tickets at Fulham v Reading on 4th May are £35 and up, so maybe not that elitist in the UK really? It's been cheaper than footie for as long as I can remember.
I’ve rarely spent more that £35. £70 for Tristan at Glyndebourne was the absolute tops. As a citizen of a land where culture is valued, Thomas should not have to spend anything like this much.