No serious study of Christianity is possible without understanding first ethical monotheism — there is one God who demands moral behavior (Micah 6:8) — and second the history of Judaism, from which Christianity emanated.
No serious study of Christianity limits itself to post-reformation or post-revivalist writings. To truly and correctly understand Christianity one must reach back to the early Christian fathers (both Nicene and ante-Nicene) and early Church history.
No serious study of Christianity limits itself to Western writings. Studying Christianity without reading the Eastern Christian fathers is like trying to pilot a ship without a rudder.
Finally, no serious study of Christianity is possible without prayer, including contemplation of how Christ unites the Divine and Human in Himself.
The following books have been helpful to me in learning Christianity, both Orthodox and non-Orthodox. They are not in any particular order of precedence.
Thompson Chain Reference Bible, Kirkbride Publishing
New Cambridge Paragraph Bible with Apocrypha (KJV), Cambridge
The Church History, Eusebius
The Great Church in Captivity, Sir Steven Runciman (review)
Biblical Literacy: The Most Important People, Events, and Ideas of the Hebrew Bible, Rabbi Joseph Telushkin
Early Christian Doctrines, J.N.D. Kelly
The Christian Tradition Volume 1: The Emergence of the Catholic Tradition, Jaroslav Pelikan
The Christian Tradition Volume 2: The Spirit of Eastern Christendom, Jaroslav Pelikan
The Kingdom of the Cults, Dr. Walter Martin
For the Life of the World, Fr. Alexander Schmemann
Christus Victor, Gustav Aulen
Three Views on Eastern Orthodoxy and Evangelicalism, Bradley Nassif et. al
God, Evil, and Innocent Suffering, John Thiel
The Virtue of War: Reclaiming the Classic Christian Tradition East and West
The Orthodox Way, Metropolitan Kallistos Ware
God and Time, Gregory Ganssle
Think a Second Time, Dennis Prager (various essays on God and morality)