I don't like Peter's Green approach on Hellenism, since it only covers the post Alexandrian political aspect. I'm more inclined for a Book covering Hellenic culture as a whole: its history since the Dark Ages, religion, politics, expanse, influences and influenced, philosophy, to how it shaped the world we live in today.
Peter Green did not set out to write a book starting from the Archaic period. The book is called "Alexander to Actium" for a reason. If you want a comprehensive narrative on how Greece arose from the end of the Bronze Age, see Robin Osborne, Greece in the Making (Routledge 2009).