These are old but likely cheap "complete in one volume" histories: Durant's
The Life of Greece is a large, detailed history which pays as much attention to social and cultural history as political and military, written by a non-specialist. Kitto's
The Greeks is more of a thematic study of Greece than a standard history but I recall it being excellent. It does work in some chronology, too. Probably the simplest, handiest one is Burns'
The Pelican History of Greece.
For Greek historians themselves (and likely moving out of the "cheap" range unless you get lucky) one of the best ways to go is with the fantastically amplified "
Landmark" series - which are like getting the book and a companion to the book in one. There are volumes of Herodotus, Thucydides, Xenophon's
Hellenika (I have, but have yet to read, that one), and even the best ancient biography of Alexander,
The Landmark Arrian. For modern biographies, I have heard bad things about the Fox Alexander, myself, but picked it up for the lavish illustrations.
I haven't read it yet, though, so I can't say. My favorite is Peter Green's
Alexander of Macedon, 356-323 B.C.. Some other biographer (J.R. Hamilton?) described Tarn as "whitewashing" Alexander and said Green "colorwashed" him. However that may be, I liked it.
And we shouldn't leave out Plutarch. Penguin has a set of four paperbacks that drops some lives and does away with Plutarch's parallelism, arranging them into chronological order so that may actually suit you but it'd probably be better just to read all the extant ones with Plutarch's "parallel" essays and so on.
Lastly, all the great poets and philosophers are essential reading, even in historical terms, if you want to go deeper into Greece (or to just enjoy some fantastic poetry and philosophy) but would obviously be overkill if you just want a single-volume overview.