In the Gospel According to St. John, I mean. Before the Last Supper.
Unless I missed a reference, he is only mentioned by name twice before Chapter 13. In Chapter 1, he meets Jesus:
Andrew, the brother of Simon Peter, was one of the two who heard John and followed Jesus. He first found his own brother Simon and told him, "We have found the Messiah" (which is translated Anointed).
Then he brought him to Jesus. Jesus looked at him and said, "You are Simon the son of John; you will be called Kephas" (which is translated Peter).
Rather passive, is Peter, particularly when compared to Philip and Nathaniel, whom Jesus meets in the next few verses. Of the four Apostles, Peter is the only one whose words aren't recorded here. In fact, Chapter 6 contains the only pre-Last Supper words of Peter recorded in this Gospel:
Jesus then said to the Twelve, "Do you also want to leave?"
Simon Peter answered him, "Master, to whom shall we go? You have the words of eternal life. We have come to believe and are convinced that you are the Holy One of God."
Jesus answered them, "Did I not choose you twelve? Yet is not one of you a devil?"
That certainly is a beautiful speech Peter gives, especially coming after verse 66, which states that "many [of Jesus'] disciples returned to their former way of life and no longer accompanied him." But Jesus' reaction is not that of Matthew 16:18; in this Gospel, Jesus has already given Simon the name Peter, and Peter's confession is no cause to bless him or praise the Father. For that matter, Simon Peter is largely elaborating on what his brother told him even before he met Jesus.
Considering just this Gospel to this point, there is no reason to think of Simon Peter as in any way distinguished from the rest of the Twelve. There is none of the "And Jesus took Peter, James, and John with Him" in John, no list of Apostles naming Peter "first." The only hint that his future career will be worth following closely is that Andrew is introduced as "the brother of Simon Peter."
But with the Last Supper discourse, Simon Peter comes into his own. He refuses to have his feet washed, then asks that his hands and head be washed as well; he tells John to ask who Jesus' betrayer is; he questions Jesus; he boasts of his fidelity to Him.
And, of course, he denies Jesus, after cutting off Malchus's right ear and following Jesus after His arrest and letting John ask the gatekeeper to let him in.
From the time "Jesus knew that his hour had come to pass from this world to the Father," Peter steps forward and becomes the key Apostle. He takes the lead, and even when the disciple whom Jesus loved runs ahead of him, Peter still enters first.
And of course it is precisely Jesus' passion, death, and resurrection that change Simon Peter from an unimportant fisherman to the chief servant of the Good Shepherd. The Gospel according to St. John conceals the figure of St. Peter almost entirely prior to Christ's hour, to an extent none of the other Gospels attempt, as though to say that it is only the light of the Passion that can illuminate Peter for the sheep of Christ whom he feeds. (A similar point can be made about "the disciple whom Jesus loved," as though the fact Jesus loved him is unimportant apart from the fact that Jesus died for him.)