I’m looking for a book which contains all (or as many as possible) of the ancient Greek myths, including the Olympian gods, Theseus and the Minotaur, the drowning of Icarus, Medusa, all those stories. I’ve found a couple “Complete World of Greek Mythology” by R. G. A. Buxton and “The Library of Greek Mythology” by Appolodorus) but I thought I’d ask for opinions and recommendations here before buying. I want something as complete as possible.
Bullfinch's Mythology is a good one. It has most western myths, including a good deal of Norse, Judaeo-Christian, and Arthurian legends on top of the Greek and Roman myths. It's more of a collection of Cliffnotes versions of the stories, but it's a good place to get a feel for the stories and work from there.
I know Stephen Fry has just released a new compendium of them called Mythos. Not read it though, or really looked into it.
You beat me to it. I was going to recommend Bulfinch's Mythology, too. It's one of the first books that usually comes up when looking for different myths. It's also been broken down into various parts so sometimes you can find a copy that's just the Greek pantheon. This is going to sound odd, but Percy Jackson's Greek Gods can also be a decent starting point. It's done in a light-hearted, fun manner, but the core of the stories are generally pretty accurate.