To ask this question is also to say that some books of the Bible are more important than others. The book of Matthew, say, is more important than, say, the book of Proverbs.
Fundamentalism argues, on the other hand, that all scripture is inerrant and infallible, and, since God wrote it and God is perfect, the Bible is likewise perfect in every way. Since one thing cannot be more perfect than another, all verses of scripture, in whatever book, are equally perfect. Leviticus 3: 16--"all fat is the Lord's"--is equal in its perfection to John 3:16 which talks of God so loving the world.
Nobody really operates on this basis. Everyone, fundamentalist or not, sees scripture through the lens of their own "canon within a canon"--their favorite books, in other words. This frames their view of the entirety of scripture and the Christian faith.
Those caveats and thoughts in place, what are the five most important books of the Bible? This was the topic of our Lenten services this year, and, my own idiosyncratic view is that they are thus: Exodus, Isaiah, Matthew, Romans, and John.
Obviously, one could make a case for other books. For example, between Genesis and Exodus, which is more important? You could make an arguement either way.
Personally speaking, I chose Exodus because of its singular influence in shaping the Hebrew story, and also because of its on-going influence through the civil rights movement and other movements for freedom.
Exodus portrays God as being on the side of the underdog. This is the earliest and arguably the most important view of God in the entire Hebrew scriptures. It's a theme that begins in Exodus and runs all the way through the prophets.
Between Isaiah or Jeremiah? Which one? My personal favorite would be Jeremiah, whose criticism of the machinations of the powerful preceded those of Jesus by 600 years, and he suffered for it, as Jesus did. That said, I must admit that, between the two, Isaiah is probably more important. Isaiah gets quoted all over the New Testament.
Isaiah had to grapple with a fundamental problem. If Yahweh was a god of war who guaranteed military victory, then why did Judah just get whupped by Babylon? Isaiah countered that Yahweh was indeed God, but that Yahweh was not a god of war, but a god who suffered on behalf of the people. Isaiah reinterpreted Yahweh, and, in the process, also gave later Christians a model for understanding the death of Jesus.
In the New Testament, my personal choice would be Mark, but I went with Matthew because Matthew has probably had more over-all influence. Mark is the earliest gospel, and provided a template for Matthew--80% of Mark is in Matthew, often word for word.
Matthew, however, in sharp contrast to Mark, takes a pro-Petrine point of view. He did this for a reason. Matthew, a Jewish Christian, was writing to, and on behalf of, a Jewish Christian community that was being increasingly marginalized as gentile Christians became more prominent in the movement. Peter, a Jew and the leader of the Twelve, would be seen as a model for Jewish Christians.
Later Christianity turned that Matthean pro-Petrinism into pro-papalism, which is contrary to the actual teachings of Jesus in Matthew (20:25-26), but an undeniably important development, nonetheless. In addition, Matthew is the most frequently cited book in the early church fathers.
You need something from Paul so I picked Romans. Some of my favorite passages are in Romans. Paul's definition of God in 4:17--"the one who gives life to the dead and calls into existance the things that do not exist"--is pure gold, and there are many others.
That said, much of it is murky, and some of his arguments don't always hold together--or, I should say, they don't hold together at my own personal level of understanding.
Romans is certainly important though. Augustine was told to "take up and read" it. John Wesley's heart was "strangely warmed" while listening to Luther's commentary on Romans being read. One of the most important theological books of the 20th century was Karl Barth's Commentary on Romans.
Finally, the fourth gospel. No other gospel so touches the hearts of the faithful as John's. Ask people what their favorite verse of the Bible is, and they are quite likely to cite something from John. Subsequent trinitarian theology is virtually dependent on the fourth gospel (though the fourth gospel also counters some trinitarian theology as well).
The earliest writings of the New Testament, those of Paul, seem to say that Jesus became Son of God at his resurrection. Mark, written twenty years later, seems to roll this back to the baptism of Jesus. Matthew and Luke, writing shortly after Mark, roll Jesus' "god-hood" back to his birth.
The fourth gospel, however, written a decade or so after Matthew and Luke, rolls Jesus divinity back to the very beginnings of creation. Subsequent theology has built an entire and very elaborate trinitarian framework primarily around certain verses in the fourth gospel.
One could argue that some of this was done in a spirit contrary to that of the fourth gospel. The accent in the fourth gospel is on loving Jesus and following him through practicing sacrificial love through the Johannine community. The focus isn't on trinitary theology, in other words, though the fourth gospel has certainly been used in such a way.
I try to say "fourth gospel" rather than "John" because, while someone named John may indeed have written it, it almost certainly wasn't John, the son of Zebedee, as is commonly supposed. It was first associated with John by Iraneus, c. AD 180, who claims that Polycarp told him that John, son of Zebedee, was the author when he, Ireneus, was a child.
Our association of John, son of Zebedee, is based on the childhood recollections of Ireneus, who, it must be said, also had his own reasons for associating each of the four gospels with prominent figures of early Christianity. It supported his arguments against gnosticism, and other beliefs he considered heresies.
For itself, the fourth gospel claims its origin in the Beloved Disciple, whoever that was. I've seen persausive cases made for both Lazarus and Mary Magdalene as the actual author. Whoever it was, they were very influential.