Peter: Peter was a lowerclass fisherman from Galilee, one of the most illiterate places in the world during a time when literacy was very low in general, even among town notaries. He could not write. He didn't write. There are a half dozen similarly dated books of Peter (Gospel of Peter, Apocalypse of Peter, etc). Writing books in the name of Peter was a cottage industry.
Paul: Only 7 of the Pauline epistles were penned by the same person (Romans, 1 and 2 Corinthians, Galatians, Philippians, 1 Thessalonians, and Philemon), the remainder are either likely forgeries or certain forgeries. At any rate, Paul was not a witness to the acts of words of Jesus and never met Jesus. He saw him in a vision much later.
John: John had his own competing ministry according to the earliest manuscripts. He is not named as the author of the gospel in his name. The only mention within the text of an author is "the beloved disciple" at the crucifixion. The only person who was referred to as that anywhere was Lazarus. The book of John dates no earlier than c. 95 AD and has a very different view of Jesus than the earlier texts, including Paul's letters. It has a different trial for Jesus and the only "high" view of Jesus's divinity. Anything that might suggest Jesus was divine, or rather, claimed to be divine, comes from this very late book.
In short, I would be cautious of basing any belief on the latest, most dubious, most different texts of the modern New Testament alone. It's ok to say "I don't know".