How to go about learning about Christianity for someone from a non-Christian background? Christianity has a huge influence on our culture and references to it come up in many literary and philosophical texts. Not to mention I really enjoy a lot of the stories like David and Golaith, Adam and Eve, Abraham and his Son for their philosophical merits.
I grew up in a non-Christian home and didn't have any real exposure to Christianity. Also I am an atheist so I am not really looking for literature "preaches but explains to me about the history and teaching of the religion. 

What texts can you recommend for someone starting out to learn about Christianity from an academic perspective? Also there are many bibles out there can you give me flavor of the "core" bibles and what they focus on and the style and context in which they are written? Thanks in advance.
A very readable overview of Christian history may be found in Church History in Plain Language by Bruce Shelley. 

A deeper dive into more recent history is Eerdman's Handbook to Christianity in America. 

For a good overview of the common beliefs shared by a majority of Christian groups, try Mere Christianity by C.S. Lewis.

For a somewhat polemical take on the contributions of the Catholic church, try How the Catholic Church Built Western Civilization by Thomas E. Woods.

The last book I will cite I have not read, but comes well-reviewed:

David Daniell. The Bible in English: Its History and Influence. New Haven and London: Yale University Press, 2003. xx + 899 pp. $40.00 (cloth), ISBN 978-0-300-09930-0. The following review should make it clear how comprehensive is the author's study of the impact of the English Bible on English culture: http://www.h-net.org/reviews/showrev.php?id=9709