Classics, A Very Short Introduction - Mary Beard & John Henderson
What I wanted from this was an answer to such questions as "What is the best source for the story of Hercules?". I still don't know the answer to that one, but I do now have a good sense of the parameters of classics as a discipline and why it matters, and a working knowledge of the Greek temple of Bassae (which provides the locus for the discussion).
The persuasive central argument is summarised as follows:
If Classics exists...in the gap between our world and the ancient world, then Classics is defined by our experience, interests, and debates as well as theirs.