The only real overview book of any quality is:

• Duffy, Eamon. Saints & Sinners: A History of the Popes. 3rd ed. New Haven [Conn.] ; London: Yale Nota Bene/Yale University Press, 2006.

However, Duffy glosses over the major historiographic disputes which have enveloped the field, so this book is less than half the picture.

When we're talking about debates about the pre-Reformation papacy, we're mainly talking about the Ullmann - Baraclough debate (Duffy does not mention the debate, and sides with Ullmann). Essentially, it's a debate as to if the development of papal hegemony was intentional or not. The relevant books are:

• Barraclough, Geoffrey. The Medieval Papacy. Library of World Civilization. New York: W.W. Norton, 1979.

• Ullmann, Walter. The Growth of Papal Government in the Middle Ages: A Study in the Ideological Relation of Clerical to Lay Power. 3d ed. London: Methuen, 1970.

However, both of these books seem, with a little distance, to have an ideological bias. As any decent scholar will tell you, when faced with an either-or argument, the answer is almost universally "both". I believe the best answer to this question is found in this excellent microhistory:

• Richards, Jeffrey. The Popes and the Papacy in the Early Middle Ages, 476-752. London ; Boston: Routledge & Kegan Paul, 1979.

If you only read one book read Richards.

The history of the Catholic Church is very closely entwined with the history of Western Europe in the Middle Ages. A good place to start might be The Civilization of the Middle Ages by Norman F. Cantor. It discusses other stuff too, but most of it is relevant to the development of the church. I wouldn't say that it goes in depth enough that it covers conclaves, etc, but it would be useful in understanding the church's role in Western civilization.

I am Catholic myself, but thought Robert Wilken's First Thousand Years: A Global History of Christianity did an excellent job of focusing on Christianity before the Middle Ages, and of not being Eurocentric. It's only 400 odd pages, and a pretty easy read. Only downside: No footnotes (although he does have extensive endnotes with citations).

Don't skip out on the Medieval stuff, of course, but it seems to me that other commenters have focused there. All I'm saying is, the Early Church is far more fascinating than many give it credit for.