Matthew 10:2-4
Now the names of the twelve apostles are these; The first, Simon, who is called Peter, and Andrew his brother; James the son of Zebedee, and John his brother; Philip, and Bartholomew; Thomas, and Matthew the publican; James the son of Alphaeus, and Lebbaeus, whose surname was Thaddaeus; Simon the Canaanite, and Judas Iscariot, who also betrayed him.
Notice that Simon, who is called Peter (literally: Rock), is referred to as "the first," despite him not actually being the first Apostle to get up and follow Jesus. We know from John 1:40 that there were at least two other Apostles who entered into Jesus' service before Peter, one of whom was his brother Andrew, but the other was not named. Therefore, since Peter was not first in order (even when listed alongside Andrew, due to the unnamed disciple who left John the Baptist's service), we must assume that Peter is first in station. This is strengthened by the fact that Peter is always listed before the other Apostles and that Judas Iscariot is always listed last and is verifiable the lowest in station.
Furthermore, Peter (as well as James and John) held privileged positions among the twelve, being a part of Jesus' inner court – invited to the Transfiguration and being set apart at Gethsemane in the Garden during the Agony of Our Lord.
Matthew 16:18-19
And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it. And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven.
Peter is the masculine form of "rock" (which is a feminine word) in Greek, and Cephas is "rock" in Aramaic. Peter is the rock on which Jesus built His Church. He also gave Peter the Keys of the Kingdom of Heaven. While he gave all of the Apostles the authority to bind and loose in Matthew 18:18, Peter was the first to receive this authority, and the other Apostles were never given the Keys.
John 21:15
So when they had dined, Jesus saith to Simon Peter, Simon, son of Jonas, lovest thou me more than these? He saith unto him, Yea, Lord; thou knowest that I love thee. He saith unto him, Feed my lambs.
Jesus commissioned Peter to "feed My lambs" three times in front of the other Apostles. He gave no one else this commission.
Acts 2
But Peter, standing up with the eleven, lifted up his voice, and said unto them, Ye men of Judaea, and all ye that dwell at Jerusalem, be this known unto you, and hearken to my words:
When the Spirit descended on the Apostles at Pentecost, it was Peter who delivered the first address to the infant Church, and it gained 3,000 initiates after his homily.
Acts 15:7
And when there had been much disputing, Peter rose up, and said unto them, Men and brethren, ye know how that a good while ago God made choice among us, that the Gentiles by my mouth should hear the word of the gospel, and believe.
There was disputing, Peter made a declaration, and the disputing ceased. Peter had the final word. Afterwards, Barnabas, Paul, and James affirm his decision.