There are a good introductions to this subject in Robin Lane Fox, The Classical World. An Epic History of Greece and Rome (Penguin, 2006), Stephen Kershaw, A Brief Guide to Classical Civilization: From the Origins of Democracy to the Fall of the Roman Empire (Robinson, 2010), and Edith Hall, Introducing the Ancient Greeks (Bodley Head, 2015).
The standard work on Athens I have used is the Joint Association of Classical Teachers' The World of Athens (Cambridge, 1984).
For the Persian Wars I have used Tom Holland, Persian Fire. The First World Empire and the Battle for the West (Abacus, 2006).