Classicist/linguist here. When I was young I absolutely loved D’Aulaires’ Book of Greek Myths, although that may be too much towards children’s literature to you.
Someone recommended Mary Renault’s The King Must Die for the Theseus myth. I would recommend all of her novelizations about the ancient Greek world. My favorites are probably The King Must Die (and I can attest that her treatment of the Bronze Age stuff was really quite good) and The Mask of Apollo, which follows a tragic actor in the declining days of Greek theater.
I also love the Iliad and the Odyssey, and my translation recommendations would be Lombardo’s Iliad-- I think his translations into colloquial English are great and easy to read. He is also interested in performing Classical literature, and I think he has an audiobook out of at least the Iliad. I’ve been to his performances many, many times, and always find them to be gripping and very moving. But my recommendation with translations in general is to flip through several, see which one speaks to you the most, and then read that.
For the Medea myth, if you can find or rent the movie A Dream of Passion, staring Melina Mercouri, I highly recommend it.
For secondary literature about Greek mythology, here are some of my favorite reads:
Calvert Watkins’ How to Kill a Dragon. It discusses the poetics of dragon-slaying myths in Greek and many other Indo-European languages, like Sanskrit, and shows how they call came from a common source in Indo-European. He also discusses a lot of other mythological and poetic material. It is soooo interesting!
Jonathan Shay’s Achilles in Vietnam. Written by a VA psychiatrist who treats Vietnam veterans, he discusses how the characters in the Iliad suffer from the triggers and symptoms of post-traumatic stress disorder the same way as the veterans he works with, and then how we can use what’s in the Iliad to improve the prevention and treatment of PTSD in the US military. It sounds weird, but it’s unbelievably good.
Walter Burkert’s works on Greek religion, like Homo Necans and Greek Religion– I found them to be really insightful and enjoyable reads.
If you’re interested in the historical period in which many of the Greek myths originated, read John Chadwick’s The Mycenaean World.
If you’re interested in the mythology of some of the Greeks’ neighbors, and people they probably had historical contact with, I recommend Harry Hoffner’s Hittite Myths.
You may have trouble getting your hands on these, since they’re papers and not books, but Stephanie Jamison’s “Penelope and the Pigs: Indic Perspectives on the ‘Odyssey’” and "Draupadi on the Walls of Troy: Iliad 3 from an Indic Perspective,” they offer really fascinating explanations of the Penelope and the bow episode in the Odyssey, and the abduction of Helen in the Iliad.
Full disclosure: Most of the people named herein are my colleagues.