You can never go astray with period writings from classical antiquity, especially those written by the Greeks. Three especially come to mind:
The Histories by Herodotus
History of the Peloponnesian War by Thucydides
The Persian Expedition (or Anabasis) by Xenophon
The Histories provides a fairly representative perspective of what your average Ancient Greek probably thought about the world and life, geographically and morally speaking. Second half of the book encompasses The Persian War, the opening of which was recently filmed in the movie 300. Quite a bit of the dialogue for that movie can be traced directly to this book. It goes on a lot of tangents and is highly speculative. Really not my favorite, but as far as knowing what your layman Ancient Greek thought, it is the most informative.
History of the Peloponnesian War provides a good historical comparison for Cold War + Vietnam and the War in Iraq, as well as a compelling realist account of power relations among states. Definitely the most intellectually rigorous of the works from classical antiquity. Drawback? The writing is verbose and can be dense.
The Persian Expedition is about how a Persian price (Cyrus) attempts to overthrow his brother (the King) with the help of 10,000 Greek mercenaries. Cyrus gets slain during battle and the 10,000 attempt to parley with the Persian king for their safe return home. Things don't work out so well; the 5 Greek commanders are captured (and later executed) during the negotiation. So the army elects new 5 commanders, among them the author (Xenophon) to lead them across many hostile territories to get back to Greece.
Probably the most compelling fact I can note about books from Ancient Greece is that they provide a lot of information on the origin and foundation for modern education and democratic-republican political systems, how these systems interact with fascist/oligarchic/Imperial systems, the partisan tensions and "personality cults" which develop in these systems, and how a military operates in said systems; Xenophon and Thucydides especially make this clear.
I would go for the Persian Expedition. Xenophon is a more accessible writer than Thucydides and doesn't meander as much as Herodotus.
I have a classics degree. Oligarchic and Imperial systems did exist, but don't bring fascism into the ancient world. That is anachronistic. (I'm not trying to be hostile, just discussing, so please don't take it that way).
Also, the system of Greece is nothing like ours in terms of freedom. The Greeks only aloud certain, wealthy adult males to vote and they had to prove their wealth in order to gain status in the
boule. Priesthoods were bought and paid for (yes, they are part of the political system) and one could buy their way into a seat in the
boule. (the boule is something like a group of senators except without any checks and balances). Plus, each city governed themselves, so the populations and land mass were far less.
Yes, there is much to gain from an understanding of ancient historians. They do under-gird some of our cultural ideals, but those ideals are more prominent in philosophers and play writes than the historians. You also have to know that the writers of Ancient Greek and Latin Literature were the very rich. They comprised some 5% of the population. That's 5% of the population governing the other 95% at their whim. So, when ancient writers speak of mundane things in a negative light, it is important to temper that with the knowledge that they are writing for the very rich, whom they normally are themselves.
All I'm saying is this: you cannot put an equal sign between our culture and the ancient Greeks. We have two different systems. This goes for the Romans as well, who are by far more parallel to our system during the time of the Republic. But what is closest to Roman culture is more like the Italian mob, who adopted that system of hierarchy in their dealings. If you watch the Godfather, it is very similar to how say Pompey would have conducted business in his own home.
Anyway, just some caution to the equation. These ancient Mediterranean cultures are bound to honor and shame, have different kinship systems, see religion in a different light, etc. There is no enlightenment, no modern dissemination of information, etc. Modern readers often project their own ideals onto the ancients by constructing something more like our culture that theirs.
That said, read them. Great works. I like Herodotus myself, but Xenophon is more accessible as the OP states (especially in Greek, although Herodotus isn't so bad either).
