Oh Great Prince, perhaps I was not clear. I said cannonization. I did not say that there were not previous texts floating around. In fact there were a lot of Christian texts in circulation...not all of which were deemed valid by mainline church members. Not all of the texts have survived. In the early years of the church there was no clear definition of Christianity...wittness the Gnostics, and the other heressies. Some Christians did not beleive in the divinity of Christ. It was no consistent understanding of what it was to be Christian.
You need to update your scholarship. First of all the Gnostics were not a Christian sect. They predate Christianity and are the product of a synchronistic view of Jewish apocalypticism and a Platonic anthropology. That they later adopted Christian characters into their texts does not make them Christian, simply one of many absorbent religions of the period. (see B. Pearson)
Further what you are describing are fringe groups that enjoyed neither popular nor geographically diverse support. While orthodox writers and communities exist from Persia to Gaul in the first two centuries of Christianity, such groups as the Ebionites, Marcionites, Montansists, and others are regionally centered and only marginally populated. Your Bauerian pluralistic view is a product of a post-modern historiography that is fundamentally ahistorical as it makes an argument from the absence of certain theorized documents.
The Emperor Constintine commissioned 50 bibles six years after the Council of Nicea. These texts became the basis for the New Testiment. As you probably know, the New Testiment was an accumulation of earlier texts. As you may also know, the New Testiment has evolved over time...that means changed.
Constantine commissioned Bibles and that there was no debate over the contents speaks for, not against, the preexistant consensus on its contents. You could try, like so many failed popular historians, to argue that Constantine's overarching power prevented dissent, but even Eusebius, the most staunch of Constantine's supporters records instances, such as the deposition of Eustantius which caused riots in spite of the emperor's endorsement. Furthermore, though Constantine tried, he could not get the people of Alexandria to even admit Arius into their city. His power over the church was minimal.
Furthermore, you cannot argue that his publishing of those texts was the "basis" of the New Testament, rather it is necessarily the culmination as it is the final step in the what you consider the formalization of the canon (though no formal act exists).
And yes, the New Testament did evolve over time. However, strangely that evolution was not toward limiting the canon, excluding heterodoxical documents as you suggest. The evolution allowed into the canon what had previously been questionable books like 2 and 3 John, Jude, Philemon, and 2 Peter. That the evolution of the canon restricted other "Christian" literature from being accepted is not only fallacious, but the exact opposite of what is historically known about the development of the canon.
The text most protestants use is the King James Version. King James made some alterations to the text to express his views better.
Which is idiotic. The current trend both in scholarship and in popular use is the adoption of the Hortian 1881 edition of the New Testament which is based off of the oldest, most reliable texts as opposed to the 14th century texts of the Textus Receptus.
We celebrate the Sabbath on Sunday not Saturaday because of Constintine.
The Christians don't celebrate the Sabbath at all. For pre-Constantinian proofs of this, see Tertullian's Answer to the Jews, the Epistle of Barnabas, Justin's Dialogue with Trypho, Cyprian's Three Books of Testimony Against the Jews, Hippolytus, and so many more. For non-Christian sources, see Pliny.
Christians celebrate the Eucharist on Sunday because it is the day of the resurrection. This is based on the
biblical example of Acts 20:7 and 1 Corinthians 16:2. Here it says "κατα μιαν σαββατου" that is the distributive use of κατα indicating the first after the Sabbath, Sunday.
There is no public independent record of a conversion by Constintine to Christianity. Thre is a record of his association with Sol Invictus...its symbols are on his coins.
The only thing known to be kept by Constantine is the title of supreme priest. However, this does not negate his favoring, participation in, and endorsement of Christianity, and certainly does not negate his baptism.
I suggest you read a church history by someone who isn't a pop-culture historian. Try not buying books based on their shiny cover at Books-a-Million.