I originally started with Athenaze but have switched to Reading Greek: Text and Vocabulary as my primary study material. I think it’s much better, I like the format and there’s more reading material, which I like. I also have the Reading Greek Grammer and Exercises and have An Independent Study Guide to Reading Greek on back order from Amazon.
This can only be decided by yourself, you choose what works best for you. I went with Athenaze.
Whatever your choice, stick with it until the end. All authors will cover roughly the same topics. The paths they follow differ of course, but overall the knowledge transmitted is more or less equivalent.
I’ve been using John White’s First Greek Book but am making slow progress. I’ll pick it back up this Fall. The reading in JACT is more conversational than in traditional texts and, although more interesting, it seems harder. I’ll keep referring to it because some of it is better presented than in JWW (and vice versa). I’m also attemting some elementary reading from the old Moss, Colson, Mayor, and Morice beginners’ readers. You can download PDF’s of these from books.Google.com or purchase new hardbound copies from online booksellers: