I’m just going to copy/paste what I have on a word document. It’s incomplete, obviously, but it does give a start to the scriptural basis of Peter’s leadership.
Note: Simon called Peter was the first Pope for the Catholic Church, and was appointed personally by Christ Himself. There are instances (below) where Peter is listed first among the Twelve Apostles, or is given permission where others are denied.
Simon Peter answered, “You are the Christ, the Son of the living God.” And Jesus said to him, “Blessed are you, Simon Barjona, because flesh and blood did not reveal this to you, but My Father who is in heaven. I also say to you that you are Peter, and upon this rock I will build My church; and the gates of Hades will not overpower it. I will give you the keys of the kingdom of heaven; and whatever you bind on earth shall have been bound in heaven, and whatever you loose on earth shall have been loosed in heaven.” – Matthew 16: 17-19
Note: “Peter”, in Greek, is Petros, while “rock” in Greek is petra. In Aramaic, “rock” is Cephas, and in several instances (below) is Peter called Cephas as a title.
He brought him to Jesus. Jesus looked at him and said, “You are Simon the son of John; you shall be called Cephas” (which is translated Peter). – John 1:42
[Christ said to Simon called Peter:] "The one who listens to you listens to Me, and he one who rejects you rejects Me; and he who rejects Me rejects the One who sent Me.” – Luke 10:16
And He allowed no one to accompany Him, except Peter and James and John the brother of James. – Mark 5:37
Six days later Jesus took with Him Peter and James and John his brother, and led them up on a high mountain by themselves [for the transfiguration]. – Matthew 17:1
“Simon, Simon, behold, Satan has demanded permission to sift you like wheat; but I have prayed for you, that your faith may not fail; and you, when once you have turned again, strengthen your brothers." – Luke 22: 31-32
Then Peter said to him in reply, “We have given up everything and followed you. What will there be for us?” – Matthew 19: 27
Note: Notice that, above, Peter is speaking as a representative (Vicar) of the Twelve.
When they had finished breakfast, Jesus said to Simon Peter, “Simon, son of John, do you love me more than these?” He said to him, “Yes, Lord, you know that I love you.” He said to him, “Feed my lambs.” He then said to him a second time, “Simon, son of John, do you love me?” He said to him, “Yes, Lord, you know that I love you.” He said to him, “Tend my sheep.” He said to him the third time, “Simon, son of John, do you love me?” Peter was distressed that he had said to him a third time, “Do you love me?” and he said to him, “Lord, you know everything; you know that I love you.” (Jesus) said to him, "Feed my sheep.” – John 21: 15-17
[To Simon Peter, Jesus said:] “Amen, amen, I say to you, when you were younger, you used to dress yourself and go where you wanted; but when you grow old, you will stretch out your hands, and someone else will dress you and lead you where you do not want to go." – John 21:18
Note: The above quote is, more than likely, a prophecy for the traditional death of St. Peter. Peter was crucified upside-down in Rome, circa 60 AD.
So they set out at once and returned to Jerusalem where they found gathered together the eleven and those with them who were saying, “The Lord has truly been raised and has appeared to Simon!” - Luke 24:33-34
During those days Peter stood up in the midst of the brothers (there was a group of about one hundred and twenty persons in the one place). He said,… - Acts 1:14
Then Peter stood up with the Eleven, raised his voice, and proclaimed to them, "You who are Jews, indeed all of you staying in Jerusalem. Let this be known to you, and listen to my words.” – Acts 2:14
Acts 2:41 - received first converts
Acts 3:6-7 - performed first miracle after Pentecost
Acts 5:1-11 - inflicted first punishment: Ananias & Saphira
Acts 8:21 - excommunicated first heretic, Simon Magnus
Acts 10:44-46 - received revelation to admit Gentiles into Church
Acts 15:7 - led first council in Jerusalem
Acts 15:19 - pronounces first dogmatic decision
Gal 1:18 - after conversion, Paul visits chief Apostle
Peter’s name always heads list of Apostles: Mt 10;14; Mk 3:16-19; Lk 6:14-16; Acts 1:13
“Peter and his companions” Lk 9:32; Mk 16:7
Spoke for Apostles - Mt 18:21; Mk 8:29; Lk 8:45; 12:41; Jn 6:69