What a thread! I hadn't seen it before, and like many others here consider J.S. Bach number one. I believe more in depth than breadth, so would thereafter go with other Baroque composers before those of other eras. But you can't eat the same thing at each meal, so would break them up with Beethoven, Mozart (perhaps a little too intellectual for my knowledge level), and some others commonly loved, even Wagner ;-).
I actually started my Classical listening with 20th Century (Stravinsky, etc.), but that doesn't wear well, does it? The Romantics bore me to death, especially Brahms. I don't get him at all.