I interpreted your wish as one for a good working grammar, which A&M definitely is. However, if you want a book to learn from, there are many candidates.
I tend to draw back from the works the newer they are, as, in my view, they tend to drift further and further from the actual linguistic issues as time progresses, issues which ought (quite naturally!) to be at the core. My advised book would be Wilding's Greek for Beginners. The work is very well set out and deals with teaching the language in an order that seems admirably sequential on logical terms.
Although the A&M is effectively a tutorial grammar, with very good notes on syntax in its last quarter, it lacks any exercises in composition or translation. Wilding, however, introduces well-scaled exercises at a very early stage. Furthermore, there are often exercises of Greek composition, which begin at an early stage, and are a superb way of really coming to grips with the language.
The book, though written long ago, is still happily in print.
Glad to see that you're ready to take the reins of both of the two horses, although perhaps they are less discordant than Plato's!