I recommend beginning with Harriet Crawford's Sumer and the Sumerians and Postgate's Early Mesopotamia: Society and Economy at the Dawn of History. Susan Pollock's Ancient Mesopotamia is excellent but very dry, as is Crawford's edited volume The Sumerian World.

I also highly recommend Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East, Treasures from the Royal Tombs of Ur, and the Early Dynastic sections of Art of the First Cities. Finally, the recent publication of Zainab Bahrani's Art of Mesopotamia has provided a very nice overview of the art of the Uruk period and Early Dynastic Mesopotamia (pp. 41-109).