The two books from iBooks are Myths and Legends of Ancient Greece and Rome by E.M. Berens and A Book of Myths by Jean Lang. Both are somewhat old-fashioned texts that are compendiums of Greek mythology. The Lang book has the advantage of also including myths from Norse mythology and Beowulf. Neither of them do the annoying practice of referring to the Greek gods by their Roman names, a habit of writers of this period. While this means kids will have to get used to Heracles as opposed to Hercules, and Odysseus as opposed to Ulysses, I much prefer this. The Lang book does use the Roman names, which is annoying.
One of the Supplimentary texts, “The Hero's Journey”, is found on a website www.mythologyteacher.com, which is a great resource to discover. (I wish I had created something of the sort.) The document is a little hard to find, but I found it under the Teaching Materials menu. There are a lot of good materials here, and I especially liked the use of Star Wars as essentially a mythological tale, which it is. Too bad I won't be using it.
I'm also expected to have a copy of D'Aulaire's Book of Greek Myths, which I have. I also want the kids to have this.
So these are the basic texts. It's not a terrible idea to use the Gutenberg texts, and frankly I think they might be a better education of the myths than The Lightnng Thief.