I think the Amorites would be a good civ, altho it would render "Babylonia" moot since Hammurabi was an Amorite. As far as I can tell, this video is a very good synopsis..
http://www.youtube.com/watch?v=WDfG4Hz8QI0
I wish the people who made that had included citations. It takes alot of independent reading to substantiate many of the claims. From my personal understanding it's very close. Great 6 minute vid. Check it out.
Also I think the Hittites would be good. They had iron working centuries before other cultures, conflicted heavily with Egypt and occupied vast swaths of territory from Anatolia to Mesopotamia.