The Rise of Athens: The Story of the World's Greatest Civilization
The Rise of Athens is a pretty good general history, concentrating sixth through the fourth centuries B.C. It isn't particularly ground-breaking; Everitt himself stipulates that he's relied heavily on such familiar sources as Herodotus and (especially) Thucydides, and anyone who's familiar with these sources won't find much that's novel in the large-scale picture. (Practically speaking, what else is there?)
On the other hand, if you're not versed on the subject, The Rise of Athens would be a good place to start. Everitt strikes a good middle ground between being hyper-skeptical and completely credulous when it comes to using those sources. The book is written in a pleasing conversational tone. The organization is basically chronological, so it's easy to follow. The main actors are scrupulously identified (and we're reminded periodically of who was who), so it's unusually easy to follow--kudos for this. There are a number of insightful asides into such topics as hoplite warfare, the cost of maintaining a galley, ancient Greek homosexuality, red-figure and black-figure pottery, and so forth.
On the third hand, The Rise of Athens follows its sources in being largely a politico-military history. It doesn't give a lot of space to Athenian drama, for example, and it gives rather less to Athenian philosophy--both areas of some significance. I also suspect that Everitt over-emphasizes the traditional Clash of Civilizations/Greeks vs. Persians/Freedom vs. Subjugation aspects of his story.
As regards the subtitle: it's hyperbole--but it's pardonable hyperbole. If you read The Rise of Athens you will occasionally be reminded that the past is an alien country. Far more often, though, you'll be struck by the similarities. The questions that the ancient Athenians grappled with--the proper relationship between the state and religion, for example, or the demands of maintaining an alliance against a common foe--are still with us. The extraordinary credit due to the Hellenes is that they were the first people whose answers to those questions are, however greatly mutated, still with us as well.