New Christians are often advised to begin Bible reading in the Gospel of Mark or John, but I might advise a new believer to begin with Philemon. I would preface the reading with some background to offer a framework for the story.
Philemon was a Christian friend of Paul who lived in Colossae. He was apparently wealthy. We know this because he owned slaves and his home was large enough to host meetings of the Colossian Church. Onesimus was one of Philemon's slaves who had run away. He got into some kind of trouble and found himself in jail. There is no indication what the problem was, but it was resolved. As Paul wrote the letter, he intended that Onesimus carry it to Philemon when he returned home.
There are important passages and meanings in this little letter. Verses 4-7 remind us of the importance of praying for those we love. Paul gives thanks to God for his blessing on Philemon and for Philemon's faith.
It appears that Philemon became a Christian through Paul's preaching, so Paul alludes to the debt Philemon owes for his knowledge of salvation. Paul, however, wants Philemon's treatment of Onesimus to be based on love not duty. He is careful to explain his position: "Please receive Onesimus because of your love and concern for him, not because you owe me a debt of gratitude."
Then Paul illustrates the principle of imputation: Treat Onesimus as you would treat me. To impute a virtue, righteousness for instance, to someone means you assume it to be true. You treat him as if you knew him to be upright and honest. Paul also uses the principle of substitution. "Treat Onesimus as you would treat me," he says. "If he owes you anything, charge it to my account. If you would welcome me, they welcome him."
This is a picture of what Jesus did for Christians. Whatever debt we owe for sins we have committed, Jesus paid. Whatever righteousness Jesus carries in his own person, he gives to us. For a new Christian or even an old one, these lessons of imputation and substitution are timeless and continuous. The meanings grow and expand as we learn and mature in Christ, but they are a wonderful way to begin.