[gbcdoj]

The best arguments I've seen for the primacy and infallibility of St. Peter and his successors are the following series of articles from Dom John Chapman's Studies on the Early Papacy:

St. Cyprian on the Church and the Papacy
St. Athanasius, Arianism, and the Holy See
St. John Chrysostom and the Apostle Peter
St. Jerome and Rome
The Condemnation of Pelagianism Part I
The Condemnation of Pelagianism Part II

These really sum up quite well the evidence from the early Church, and the article on St. John Chrysostom also treats of the Scriptural evidence through his interpretive grid. Well worth reading.

[ImaGraftedBranch]

Even better here:

Jesus, Peter & the keys A Scriptural Handbook on the Papacy

It is 431 pages long. There are no doubts after reading this and the bible together.