The Robert Fagles translations of the Iliad and Odyssey are widely considered to be masterpieces: whether or not they are the best is a matter of opinion. I think they'd be hard to beat. Lattimore's translations are also very good. Generally speaking, the older the translation, the more difficult you'll find it. Pope's translations, for instance, are classics, but can be a hard slog for the modern reader.
So go with Fagles, absolutely. The introductory essay by Bernard Knox is a worthy read in its own right. For some background to the period you simply must read Helen of Troy by Bettany Hughes. This is not one of those historical fiction autobiographies but a fantastic exploration of the late bronze age and the roles that Helen hasa played in our myths and legends.
Here are some googlebooks previews, which seem to include the entire introductory essays by Knox. Joyeux Noel.
http://books.google.com/books?id=TpS...fagles#PPP1,M1
http://books.google.com/books?id=lZW...=robert+fagles
P.S. Ajax is mainly a character in the Iliad, not the Odyssey.
P.P.S. Don't sweat the Greek: even the Greeks themselves needed special help to read Homer.
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