Reddit reviews Metamorphoses (Oxford World's Classics)

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.