Then Homer. Opinions vary on which translation of the Iliad is best (and it makes a huge difference). I'd stay away from Pope which is more of a remake than a translation. Lombardo is very modern. Lattimore is typically used for academic purposes. I would recommend Fagles.
After that, it depends on what you're into.
Philosophy? Pre-Socratics -> Plato -> Aristotle. What you choose here again depends on what you're into. There's politics, metaphysics, ethics, aesthetics, etc.
History? Herodotus -> Thucydides -> Xenophon (The Landmark series for all 3)
Theater? Oresteia, Medea, the Theban Cycle.
Mythology? Hesiod.
It covers the unity of the Greeks, their heroic outlook, the gods, the city and the individual, the good man and the good life, myth and symbol, imagination and reality, the plastic vision, and the place of reason.
https://www.youtube.com/playlist?list=PLHxtyCq_WDLXzT_CgYPtj...
Unfortunately, it would be easier to consume as audio files as the video adds little. The lectures to date have been on the Greeks but the course is ongoing and will come up to more modern times, ending with Martin Luther King.
I would recommend it to anyone who wants to trace the thoughts of the Greeks forward to WW2 era-ish, thoroughly enjoyable read.