The thing is, "ancient Greek literature" is rather a broad field. You have long, traditional mythological epic like the peoms attributed to Homer, then you have recreations of that with a quite different background, mindset, and agenda, as in Apollonius Rhodius' Argonautica. You have tragedy which takes traditional stories and uses them in particular ways to explore particular things; and you have different forms of comic theatre: Aristophanes is satirical, very nudge-nudge-wink-wink, but hard to understand with notes in the same way modern topical comedy will be in a 100 years time; Menander (little survives, but his style was taken up by Plautus and Terence in Latin) is more comedy of manners and less time-bound. You have short lyric poetry (lots of it in pieces - of Sappho, for example, we have at best two or three more or less complete poems) that can be about almost anything; and you have stylized, allusive, public poetry (Pindar), and you have short epigrams about sex and love (Book 12 of the Greek Anthology is filled with the stuff, mainly [male] homoerotic). You have historical narrative (Herodotus - a great storyteller, Thucydides - difficult and complex, Xenophon) and biography (Plutarch), and you have fictional narrative (Longus, Achilles Tatius, Heliodorus - the so-called "novels", relating the adventures of young [different-sex] couples), and everything in between (Xenophon's Cyropaedia, a fictionalized treatment of a historical figure). You have comic dialogues, like Lucian's Dialogues of the Courtesans. If you're into myth, Hesiod will be as interesting as Homer; so will the ancient handbooks like Apollodorus' Library. Philosophy can be serious and technical (Aristotle) or more entertaining (the shorter, more famous Platonic dialogues - and a different view of Socrates comes from Xenophon's ones).
Also, there is a LOT of ancient Greek literature on the Web, but too much of it is in old translations: these aren't bad, but they were written in and for their time and can be inaccessible in style, language, etc., so rather try to find versions published in the last twenty years or so - you will find the style, and the range of notes and such, different and often more accessible or in tune with modern interests. Also, remember than translation is an art, not a science, and translators have their own style: if you don't find one version of, say, the Iliad or Odyssey appealing, try a different one - there is no shortage of them (in verse, Lattimore, Fitzgerald, Fagles, Mandelbaum; in prose, Rieu, Hammond). The same goes for most of the really well known writers.
By the way, it's one "l" in Iliad (as in "Ilion"="Troy")!