I've been starting and stopping my greek studies for a couple of years now. Since research of textbooks and "best method" is a great procrastination, I've became familiarized with several books and ideas for self-teaching of greek and language in general
One of the first things I came by was this list
which is discussed in this recent post
and thought he sounded like he knew what he was talking about; so I became intrigued by the fact that the book he suggests as the best course for homeric greek (Schoder and Horrigan) is out of print, and extremely hard to find.
As luck would have it, I've found volume 1 of the 2nd revised edition (1985) in a library, and volume 2 of the same edition is not hard to find.
I've done the first twelve lessons of book 1 and this is my opinion:
First, it is absurd that this book is out of print. It is by far the best book I've seen (and used) on learning greek.
Pharr, which is well respected and well thought of, is in my opinion a very, very bad way to start learning greek. It is hard on the eyes, at times boring, at times dreary, unwieldy, old, old school, and poorly revised course. It's grammar, for consultation, is worth the price of the book, though.
Since I agree that starting with Homer is the best way to learn the language, that doesn't leave one with too many options (the only mention of Beetham's Beginning Greek with Homer in Textkit I could find is not encouraging).
Second, I don't think the new edition is on the whole an improvement
as I've compared a couple of pages, and thought the 2nd ed more welcoming. It (the 3rd ed) might have many valuable corrections, but the spirit of the writers, imprinted on every idea and suggestion, and in those lovely quotes at the beginning of each lesson, was effaced. Plus, the second volume is now due only in 2008. But if you have the 3rd, it's still better than other titles.
The answer key for the 2nd edition is, as Buadhaigh said, very hard to come by. But the link he posted solves this. Btw, thank you, Buadhaigh!