Reddit reviews Iliad, Odyssey, and Aeneid box set: (Penguin Classics Deluxe Edition)

I would start with Ovid, he writes about Roman myth which is practically the same. Also read some Homer. I can recommend more books when I get home.

Edit: I would start off with Mythology by Edith Hamilton. This will give you a good run down of who is who and she gives you the Greek and the Roman names. I would then move on to read the three classic epics by Homer and Virgil. Finally I would move to Ovid and read Metamorphoses. From there I would read what ever you can get your hands on.

The Fagles translation was recommended to me by a friend who is a fan of them. I picked up this box set from Amazon about a year ago and have neglected to get around to reading it. It's been far too long since I've revisited some classics, and hit up some that I've never read before. Last time I read Homer was in high school.

My extended list would see some Shakespeare, Chaucer, Sturgeon, Van Vogt, Bester, Dick, and more Neal Stephenson in there.