The term “Ancient Persia” covers three great empires – the Achaemenid, Parthian and Sasanian empires.
Websites
The main source I have used has, for a change, been a website This is:
Encyclopedia Iranica Online
This has numerous superb scholarly articles on every conceivable topic to do with this subject. I have plundered it mercilessly, and would like here to express my gratitude to it. A word of warning – not for the reader looking for a general overview.
Wikipedia of course has vast amounts of information on the topic. The gateway page is Ancient Persia.
The Met Museum website has very readable summaries of the histories of the Achaemenid empire, the Parthian empire and the Sasanian empire.
Books
For books, my main source on the Achaemenid empire has been:
Cook, JM, The Persians, Dent, 1983 – this is a readable and scholarly account of the Achaemenid empire.
Also of use have been:
Roaf, M., A cultural atlas of Mesopotamia and the Ancient Near East, Andromeda, 1990,pp. 203ff. – offers a superbly illustrated and highly informative survey of the history of the Achaemenid empire, with an emphasis on its archaeology.
A lavishly illustrated work on archaeology for the general reader which includes good coverage of ancient Persia, is Renfrew, C. (ed.), Past Worlds: The Times Atlas of Archaeology, Times Books, 1995; p. 158-9 deals with the Achaemendi empire, p. 186-7 with the later ancient Persian empires.
For an insightful look at government of the Achaemenid empire, see Finer, S. E., The History of Government, I, Ancient Monarchies and Empires, OUP, 1999, p. 286ff.
Some recent books (which I can’t vouch for yet but get very high ratings) offering introductory surveys to all the great Persian empires of antiquity, are:
Wiesehofer, J., Ancient Persia, Tauris, 2006.
Vansan, A., Ancient Persia, 2012.
Curtis, J., Ancient Persia (Introductory Guides), 2001.