For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
Derek Blake
In my opinion, I would start with reading Genesis, which gives a new Christian the basis of our faith and why there was a plane in God's mind, and a need, for Jesus. After that go on and read the Gospels; Matthew, Luke, Mark, in that order. Later one can return to John's Gospel, as this is more about the Spiritual Meat, maybe after reading Exodus, and perhaps the Book of Job, very revealing.
Peggy Johnson
I started with Hebrews....followed by the Gospels then to Genesis.
Daniel Veler
I would begin with 1 John. Read all of his writings; you will come to know if God truly abides in you.