if you want to learn about the greek civilization you should read the ancient greek literature...
Herodot "Histories"
Thukydides "The Peloponnesian War"
Xenophon "Anabasis", "Hellenika"
the list could go on and on.
you would never imagine, that the ancient people could tell such thrilling stories, that give you an imagination of how their world used to be.
Oh, I can imagine it....humans have had the same basic intellectual equipment for what.... 200,000 or more years... The problems, though, of dealing with the past are essentially threefold....having material to analyze; communication...understanding the language, or even the word meanings that were being conveyed...even if it is ancient Greek or Latin; ...and most significantly, the amount of material that has been lost down through the ages....either inadvertently or otherwise....
Oh, and thanks to the OP...an interesting thread...
Robin Lane Fox wrote a good and extremely scholarly, if unimaginatively titled, biography of Alexander the Great which may be of interest. Similarly, Appian's Campaigns of Alexander.
I would say that you're approaching it the wrong way: 'classic' works of history should not be read by laymen as history books (although historians can find them useful); they should be read as literature. Sallust and Tacitus - just off the top of my head - write in beautiful prose, and they and others such as Suetonius and Plutarch create vivid, compelling characters and speeches from historical events - read a modern book to learn what happened, then enjoy the classics almost as if they were fictional.
EDIT: just seen Kyrou Anabasis mentioned above - as a work of history, that one doesn't even pretend to be serious.