A Suggested Integrated Reading Web of Pre-Christian Literature
1) The Main Greek Myths - a necessary starting place. Not the obscurities, but the dear old favorites, if they are or have become unfamiliar. Jason and the Argonauts, Theseus in Crete, Perseus and Andromeda, the Birth of Venus, Dionysos and the Pirates, and the like. Young Ancient Greek children heard these culture-cores from mothers and grandmothers, in that sense the women were the keepers of culture, while the men found ways to amplify the beauty through various mediums. Don't start with something dry, no Robert Graves or anything like that. Go with a compilation intended for children and perhaps supplement that with a book graced with poetry such as A.Guerber's Myths of Greece and Rome.
2) The Odyssey. This is and was surely the most-read and referred to work of Ancient Greece and is therefore useful further background reading. Choose a translation you feel comfortable with as it's a long book.
3) Having read The Odyssey you're in a position to enjoy a work that includes comic references to it, such as the genius Aristophanes' Wasps or Euripides' Cyclops. It should be said however that Cyclops is the closest you can come to throw-away Greek theater and its value lies in giving us at least some insight into the nature of the satyr play. But getting into Aristophanes at this early stage is a great idea. Barrett's translations are fun and being from the sixites their language brings the Monty Pythonesque side of Aristophanes out to the full.
4) If you enjoyed Aristophanes' Wasps then there are ten other surviving plays by him to choose from. This is the guy who first suggested we make love not war, that we'd be better off if women had the vote, more advanced kitchen appliances instead of slaves, and who payed posterity the immense service of providing a lovable, comic, Athenian version of the god Dionysos in perhaps the greatest of his masterpieces, The Frogs. The 'I need to dump my load' gags at the beginning work better now that we have an equivalent phrase in English, and so the more recent translation by Kenneth McLeish is worth a read.
5) More Aristophanes, check out his Clouds, enjoying the humourous image of the philosopher Socrates...
6) ... then get a more accurate picture of Socrates through some Plato: if you now read Plato's Symposium through then you'll get, in the latter parts, a true inisight into Platonic philosophy whilst also meeting your new friend the comic playwright Aristophanes, who turns up as one of the characters, complete with a rather amusing piece of philosophy, just as Socrates turned up in Aristophanes Clouds.
7) The Frogs has introduced you to this lovable and surprisingly human vision of Dionysian genius, and if you want to continue with more that is lovable and Dionysian then you could read your first ancient novel, the wonderful Daphnis and Chloe, and this will give you a sensous expression of the philosophy of Love expressed by Socrates in the latter parts of Plato's Symposium in action. Surely the best reading for a long, relaxed Aegean island-hopping holiday. To be savoured.
8) Some pastoral poetry - if you go to the First Idyll of Theokritus you will find
more on Daphnis, his death, as it happens, but don't worry, because then you can go to Virgil's Fifth Eclogue and you'll get his apotheosis.
9) Now that we've started on the poetry, you could delve further into one of the most delicious storehouses of ancient literature, that of Greek lyric poetry with its long list of poets from Archilochus in the seventh century right through the Golden Age, on through the Hellenistic period and then to the Romans who took up the baton. Included in this collection are the works of famous poets such as Sapho and Catullus, and even the odd one or two attributed to that same Plato whose Symposium you have read, just to keep it in the family.
10) Daphnis and Chloe, the novel you have now read, grows out of a description of a painting. What about something a little unusual? Philostratus' Imaganes describing paintings in an ancient gallery in Naples might sound dull, but isn't. No Ancient Greek paintings have survived, but according to the reports their realism was of the same degree of excellence that they managed in their statues. We can only imagine. Some very fine Roman paintings survive, however, many of which were based on Greek originals. I would recommend getting hold of a large colour picture book of the art and architecture of Pompeii.
11) If you're going to go ahead and read that other novelistic masterpiece, The Ethiopian Story, then why not start with a bit of Herodotus. For goodness sake don't try to read his Histories all through, but have a look at the intriguing section on Egypt.
12) The Frogs introduced you to the playwrights Euripides and Aeschylus, as characters, so why not have a look at some of their own work, perhaps Aechylus' heavy Orestes trilogy, and then the lighter but seminal Alkestis of Euripides.
13) With all of the above under your belt you will get more out of The Ethiopian Story. It's crying out to be made into a film, which will no doubt happen one day, but it won't be possible to get from a film that same sense of a work integrated with the library of anitiquity that we can get from the book.
There are of course many, many more great works from antiquity; I've mentioned the above because they can be read as one integrated group, a kind of reading web covering works from the dawn of European literature to the end of antiquity.