I think I can help with your question here. I'm a retired university professor who's been an audiophile and classical music and opera buff for 40 years. In addition to having a large classical and opera CD collection, I've been attending live performances of operas for more than 40 years, and I've helped a number of "new to opera" persons like yourself get into opera.
I recommend starting with Puccini's La Boheme, and I'd recommend the Decca/London recording with Tebaldi and Bergonzi, Tullio Serafin conducting. This is an opera that everyone seems to love; it has probably "hooked" more people just getting into opera than any other opera. This recording has excellent singing and excellent sound. It has the additional advantage of being budget-priced and being available in either a "highlights" version (1 CD) or the complete opera (2 CDs). The Freni/Pavarotti/von Karajan version, also on Decca/London, is also very good, although I don't like it as well as the more idiomatic Serafin version.
For a second opera, I'd recommend Puccini's Madama Butterly, and again I'd recommend the Decca/London recording with Tebaldi and Bergonzi, Tullio Serafin conducting. Again, this one is another great favorite with almost everyone, and again, this recording has excellent singing and excellent sound, and has the advantage of being budget-priced and being available in either a "highlights" version (1 CD) or the complete opera (2 CDs).
After these two for openers, I'd recommend Verdi's La Traviata, in the Decca/London recording with Sutherland, Bergonzi, and Merrill, Sir John Pritchard conducting. This is perhaps the most popular of the Verdi operas, and again this recording has excellent singing and outstanding sound, and has the advantage of being budget-priced and being available in either a "highlights" version (1 CD) or the complete opera (2 CDs).
You mention Carmen, and that's a good place to start with French opera. I'd recommend the Troyanos/Domingo/Solti recording on Decca/London. Carmen is the most popular of the French operas, and again this recording has excellent singing and excellent sound. The complete opera is 3 CDs, but a single-CD "highlights" version is available.
For a second French opera I'd recommend Gounod's Faust, in the Sutherland/Corelli/Ghiarov/Bonynge recording on Decca/London. Faust is another perennially popular opera, with a terrific, smashing grand finale (quite spectacular in this recording). Again, first-rate singing and excellent sound. The complete opera is 3 CDs, but a single-CD "highlights" version is available.
For a Mozart opera, I'd recommend Don Giovanni in the Wachter/Schwarzkopf/Sutherland/Giuilini recording on EMI. Don Giovanni is the greatest of the Mozart operas, and this is a beautiful, very well-sung performance of it. The complete opera is 3 CDs, but a single-CD "highlights" version is available.
I've tried to limit these few recommendations to (1) operas that are very popular, appealing, and accessible; (2) recordings that have excellent singing; and (3) recordings that have first-rate stereo sound. The famous recording of Puccini's Tosca (2 CDs) with Callas/Di Stefano/Gobbi/De Sabbata on EMI is one of the greatest opera recordings ever made (some think it is the greatest), and Tosca is a very popular opera, but be forewarned that this recording has dated 1950 monaural sound.
Finally, I'll point out that Carmina Burana, which I too enjoy very much (I've got several good CD versions) is not an opera. It's a cantata. An opera is a play, a drama, set to music, requiring soloists, chorus, and orchestra. A cantata like Carmina Burana also requires soloists, chorus and orchestra, but it's not a play and is essentially static onstage.
Incidentally, I've found that an excellent way to buy the CDs I've mentioned above is on Amazon.com, from the many Amazon.com "marketplace sellers" that sell used and discount-priced CDs listed there. I have no connection with Amazon.com (although I've written a number of reviews for them), but I've been buying my CDs there for the last two years, have been very pleased with the service, and have saved a lot of money. Definitely worth checking out.
Hope this offers some specific help. Happy listening!
I recommend starting with Puccini's La Boheme, and I'd recommend the Decca/London recording with Tebaldi and Bergonzi, Tullio Serafin conducting. This is an opera that everyone seems to love; it has probably "hooked" more people just getting into opera than any other opera. This recording has excellent singing and excellent sound. It has the additional advantage of being budget-priced and being available in either a "highlights" version (1 CD) or the complete opera (2 CDs). The Freni/Pavarotti/von Karajan version, also on Decca/London, is also very good, although I don't like it as well as the more idiomatic Serafin version.
For a second opera, I'd recommend Puccini's Madama Butterly, and again I'd recommend the Decca/London recording with Tebaldi and Bergonzi, Tullio Serafin conducting. Again, this one is another great favorite with almost everyone, and again, this recording has excellent singing and excellent sound, and has the advantage of being budget-priced and being available in either a "highlights" version (1 CD) or the complete opera (2 CDs).
After these two for openers, I'd recommend Verdi's La Traviata, in the Decca/London recording with Sutherland, Bergonzi, and Merrill, Sir John Pritchard conducting. This is perhaps the most popular of the Verdi operas, and again this recording has excellent singing and outstanding sound, and has the advantage of being budget-priced and being available in either a "highlights" version (1 CD) or the complete opera (2 CDs).
You mention Carmen, and that's a good place to start with French opera. I'd recommend the Troyanos/Domingo/Solti recording on Decca/London. Carmen is the most popular of the French operas, and again this recording has excellent singing and excellent sound. The complete opera is 3 CDs, but a single-CD "highlights" version is available.
For a second French opera I'd recommend Gounod's Faust, in the Sutherland/Corelli/Ghiarov/Bonynge recording on Decca/London. Faust is another perennially popular opera, with a terrific, smashing grand finale (quite spectacular in this recording). Again, first-rate singing and excellent sound. The complete opera is 3 CDs, but a single-CD "highlights" version is available.
For a Mozart opera, I'd recommend Don Giovanni in the Wachter/Schwarzkopf/Sutherland/Giuilini recording on EMI. Don Giovanni is the greatest of the Mozart operas, and this is a beautiful, very well-sung performance of it. The complete opera is 3 CDs, but a single-CD "highlights" version is available.
I've tried to limit these few recommendations to (1) operas that are very popular, appealing, and accessible; (2) recordings that have excellent singing; and (3) recordings that have first-rate stereo sound. The famous recording of Puccini's Tosca (2 CDs) with Callas/Di Stefano/Gobbi/De Sabbata on EMI is one of the greatest opera recordings ever made (some think it is the greatest), and Tosca is a very popular opera, but be forewarned that this recording has dated 1950 monaural sound.
Finally, I'll point out that Carmina Burana, which I too enjoy very much (I've got several good CD versions) is not an opera. It's a cantata. An opera is a play, a drama, set to music, requiring soloists, chorus, and orchestra. A cantata like Carmina Burana also requires soloists, chorus and orchestra, but it's not a play and is essentially static onstage.
Incidentally, I've found that an excellent way to buy the CDs I've mentioned above is on Amazon.com, from the many Amazon.com "marketplace sellers" that sell used and discount-priced CDs listed there. I have no connection with Amazon.com (although I've written a number of reviews for them), but I've been buying my CDs there for the last two years, have been very pleased with the service, and have saved a lot of money. Definitely worth checking out.
Hope this offers some specific help. Happy listening!