The Bible is not strictly written in chronological order. For example, the book of Job belongs in the time frame of the book of Genesis.
The Old Testament foretells Jesus and the New Testament is fixated on Jesus, a new Christian or a non-believer should start their reading with any of the four gospels.
The Gospels are great books to read from start to finish, instilling the sense that Jesus is alive in everything we do, and not just a historical figure. The Gospels help readers discover Jesus, learn of his miracles, and see how he lived his life.
So, I believe the new believer should begin by reading one or all of the gospels. Once the gospels have been read, I would read Genesis. This is important because Genesis reveals the origins of the people of God and illustrates the fall of mankind and the costs of disobedience. This outlines the need for salvation and the need for man to repent.
Here is an ideal order for a new Bible reader:
1. The Gospel of John
2. The Gospel of Mark
3. I John
4. II John
5. III John
6. Genesis
7. The Gospel of Luke
8. The Gospel of Matthew
9. Romans*
10. Psalms
11. Proverbs
*Everyone Should Read Romans!
Romans gives a clear portrayal of all views the Bible affords. Scholars say that in a way, all the books of the Bible lead to Romans. Romans is a book of truth about God, taught by God. Paul wrote to the Roman church to explain how the gospel works. In Romans, Paul explains Jewish law, grace, salvation, and more.
Every Christian should read Romans at least once in their lives to get an idea of the main themes of the Bible: God, sin, judgment, faith, grace, the Christian hope, and the nature of the church. Romans is a comprehensive doctrine, a book of life, and a book of the church.
Romans pulls it all together!