I suspect you would wind up with a series of books, or at least a set written by different authors, as Iraq has quite a bit of history, to put it mildly.

For my period, I would recommend Babylon by Joan Oates or A History of the Ancient Near East as an introduction, then perhaps a book on the Persian empire, which there are many suggestions here

Then we are getting out of my area, but hopefully some other Islamic and preislamic scholars can chime in.