This might interest you (I have a degree from here)
I recommend beginning with Homer, Hesiod, and the Historians (Herodotus and Thucydides). The Iliad and Odyssey held the same place as the bible for Greek culture, and the historians present a unique look into the political and ideological background on Greek philosophy burst onto the stage. You also may find the philosophers difficult if you have not done some geometry with Euclid. They refer often to geometric metaphors taken from mathematicians like Euclid. High school geometry will not be very helpful for understanding greek philosophy, as you will find out for yourself.
Once you have perused these, I would recommend starting with Plato’s Theatetus, Gorgias, Republic, Apology-Crito-Phaedo (they form a kind of trilogy), symposium and Meno. The Parmenides, Sophist and Timaeus are a little more esoteric and weird, if you ask me. Not good starting places. I recommend you read the Nichomachean Ethics for your first Aristotle, since it is the most inspiring and accessible, as well as a good model for his style of inquiry. There is a canonical approach to Aristotle that starts with the “logic,” or “organon,” and then goes to the Physics, Metaphysics, On the Soul, Ethics, Politics, Rhetoric, and Poetics. For translations, I recommend Eva Brann for Plato (especially the Phaedo), and Joe Sachs for Aristotle. Where you cannot find these, I recommend using a solid, 19th century translation, like the Jowett for Plato. Another good Aristotle translator is Apostle.
If you ever have any interest in pursuing this, I have found Aristotle to make a lot more sense in Greek. Translations of his works either use a lot of latin terminology or use tons of compound words and glossaries. In his own language, he is one of the clearest writers there is.
If that sounds like too much junk, just start with the apology-crito-phaedo trilogy, then move to the Theatetus and Symposium. Then read Nichomachean Ethics; go from there. Hope this was helpful.
Ulitimately, I have to agree with Iilikoi. You just kind of have to dive in. Pick one book, and read it. If you like it, read more. Good luck!