Ok Dan, you post tons of helpful info all over these forums, so the least we musical types can do is make some decent suggestions. I'm sure Franks and Stella will chime in here at some point too as they too are classical sorts of folks(Franks is doing grad work at Indiana and plays bass in the orchestra and Stella played violin for many years).
I myself am an opera singer and classical pianist trying to make a living as a professional musician...yikes!
I definitely second the Brandenburg concerti of Bach. When he wrote those he was conducting an orchestra made up of virtuoso musicians so the pieces are exceptionally difficult and also striking beautiful. Vivaldi is also another good suggestion, although after awhile all his music starts to sound alike.
The Flower Duet is from Bizet's opera Carmen and is faaaaaaar from being baroque, so I will assume you're open to more modern classical music(post 1815). If you speak any foreign languages, look for operas in those languages as it will be the most rewarding for you. Also, opera is best enjoyed live! I sing this stuff every day and get bored shitless when I listen to it, but I could watch it all day long and never get tired. Go see something live and then buy a CD of that opera.
There are many opera compilation albums out there that are worth buying, especially for people new to the genre. One I like is called "Simply the BEst Night at the Opera" and is a 2-cd set for only about 17 bucks. Another is called "The Best Opera Album Ever" and is also worth buying. Some tracks overlap between teh two, but with different artists singing. If any of the singers or tracks stand out to you, then look for more recordings by the same singer and/or composer. The genre is so vast that I work in it and still haven't seen or heard half of what must be out there. I could list all my favorites, but this post is getting long enough already and you'll enjoy things much more if you develop your own tastes. So, the compilation albums are the way to go. OH!!! And AVOID the opera in english albums, unless the opera was originally written in english! These usually have not so great singers on them and you still can't understand a damn thing they're saying for the most part.
Hope this helps Dan. If you have any questions let me know and I'll try and answer them. I can make more specific suggestions if you'd like, but this oughts get ya started for relatively little money. Oh, Kazaa also has lots of classical stuff...just search by the composer's name and see what ya find. Ciao!