I've done a fair amount of general reading on Sumer and come away with a vague impression of a transition over the Early Dynastic period from rule by temples to rule by secular monarchs. I'd be really interested to find out what the current thinking about this is (I don't even know if this view is still widely accepted), what led researchers to this conclusion and more details, assuming any exist, on the political processes underpinning Sumerian city-states. I'm particularly keen on the Early Dynastic period but earlier periods are also of interest. Recommendations for further reading material of any kind would be greatly appreciated. Thanks in advance!
I recommend beginning with Yoffee's Myths of the Archaic State: Evolution of the Earliest Cities, States, and Civilizations and Pollock's Ancient Mesopotamia.
Death Rituals, Ideology, and the Development of Early Mesopotamian Kingship by Andrew Cohen is a very good study of the intersection of politics and religion in early Mesopotamia.
It's a very dense read even for archaeologists, but The Political Landscape: Constellations of Authority in Early Complex Polities by Adam Smith provides an overview of the relationship between political configurations and landscape. He draws upon a number of societies, including Mesopotamia, Urartu (in modern Turkey/Armenia/Iran), and the Maya kingdoms.
For the Sumerians in general, Crawford's Sumer and the Sumerians (2nd edition) and the edited volume The Sumerian World remain the best resources. Liverani's The Ancient Near East: History, Society and Economy, Van de Mieroop's A History of the Ancient Near East, and Postgate's Early Mesopotamia: Society and Economy at the Dawn of History may also prove useful.
Finally, for comparative works, there's A Comparative Study of Six City-State Cultures edited by Mogens Hansen and the follow-up volume A Comparative Study of Thirty City-state Cultures. Also check out Trigger's magisterial Understanding Early Civilizations, which I cannot recommend highly enough. His book focuses on Early Dynastic Mesopotamia as well as Old Kingdom Egypt, the Maya, the Inca, the Aztecs, Shang China, and the Yoruba.