From HKH?, "Appendix: When All We Can Do is Read" at page 259:
[The] private acquisition of Greek wisdom relies more than ever on the individual's self-taught education – the reading of the Greeks themselves and general books on Classical Greece. . . . [T]he following 10 primary works serve as well as any as an introduction to Greek thought and includes a fascinating literature mostly unknown to the reading public.
Here are the "10 primary works" (pp. 259 - 266), but without Hanson and Heath's annotations:
Homer, Iliad, translated by Richmond Lattimore (Chicago: University of Chicago Press, 1961). This is the Iliad I read in translation at Duke in a sort of "great books" course taught by the president of the university. The link, however, is to a 2011 edition on Amazon that has the same translation but a lot of supplementary material by another writer. Abe's Books is where to find a used 1961 edition. The Lattimore translation is also part of Great Books of the Western World and we have a set. However, I want to read the Iliad again. When I read something like this, I like to pencil small checkmarks and brackets and now and then a note. I don't want to do that in The Great Books hardback, so I'm getting a used paperback from Abe's to take around with me.
Hesiod, Works and Days, translated by M.L. West in Theogony: Works and Days (Oxford: Oxford University Press, 1988). The link is to that very translation on Amazon, an inexpensive paperback that, with a Prime membership, gets you a brand new copy for about the same as a used copy on Half.com or Abe's. I always check Amazon first, and then go to the used booksellers.
Archilochus, Poems, translated by Richmond Lattimore, in Greek Lyrics (Chicago: University of Chicago Press, 1960)
Sophocles, Ajax, translated by John Moore in Sophocles II, edited by David Grene and Richmond Lattimore (Chicago: University of Chicago Press, 1957)
Euripides, Bacchae, translated by W. Aerosmith, in Euripides V, edited by David Grene and Richmond Lattimore (Chicago: University of Chicago Press, 1959).
Thucydides, The Peloponnesian War, translated by Richard Crawley as The Landmark Thucydides, edited by Robert Strassler (New York: The Free Press, 1996)
Old Oligarch (Pseudo-Xenophon), The Constitution of the Athenians, in John Moore, Aristotle and Xenophon on Democracy and Oligarchy (Berkeley: University of California Press, 1975)
Aristophanes, Lysistrata, edited by W. Aerosmith in Four Comedies by Aristophanes (Ann Arbor: University of Michigan, 1969)
Plato, Apology, translated by G.M.A. Grube, in The Trial and Death of Socrates (Indianapolis: Hackett, 1975)
Demosthenes, First Philippic, in Greek Political Oratory, edited and translated by A. N. Sanders (New York: Penguin, 1980)
(Note: One might ask, did I laboriously keyboard each and every one of those citations? No. With book in hand, and the Dragon software engaged, I dictated the list. I'm getting pretty good at it.)