Start with Xenophon, which is what they’d start school boys on for Greek translation. Either read his dialogues with Socrates, his “education of Cyrus” (hey, non-western!) or “Anabasis.” The last one is probably the most exciting.
Alternatively, Herodotus is fun, but you won’t read the whole thing. It is good to dip in and out of. Oh, Plutarch’s “Life of Alexander (the great)” is not too long and better than a history, because he focuses on his character and telling personal stories.
Once you get going, Plato is frikkin amazing. But you have to want it— or have a guide or group. I personally like “the Parmenides” because it is mind bending. Or the symposium to hear from a brilliant lady philosopher about the nature of love.
Oh, then if you want something fantastic, read Iamblicus’ “Life of Pythagoras.” It is very well written and will change your concept of the western world.