Thank you for the question on canonicity, “Who decided which books should be included in the Bible & which didn’t make the cut?”
In my opinion, it is not the matter of who decided which books were consider Scripture or not Scripture, but how did the early Church accepted or rejected the many scrolls or books. One can read the list of the Apocrypha and the Pseudepigrapha.
The early church had Christian centers as in Jerusalem, Alexandria, Ephesus, Rome, and Constantinople. Each region had its own bishop who superintendent the churches in that area. It is more than likely that it was those regional bishops who decided what was Scripture among the writings that were available.
One must also remember that from time to time the Roman emperors would persecute the Christians and the Churches since they did not give their allegiance to Caesar or to the Roman gods, but to Jesus. This made it difficult for the churches to be consolidated into one entity.
In addition, the scrolls or letters were not collected into one book whereby churches had a copy of that one book. Churches may have a copy of a letter but no church had all the letters of the what is now known as the New Testament. It is similar of Jewish synagogue may have a scroll of one of the books of the Old Testament, but not the whole Old Testament. The Ethiopian Eunuch returned to his home with the Book of Isaiah, not the whole Old Testament.
Thus it can be assumed that different regions may accept one book while another region may not accept it as Scripture as the Gospel of Barnabas or the Gospel of Thomas. This would also apply to the Old Testament scrolls as some accepted Esther as Scripture while others questioned or rejected that scroll as Scripture. In the Qumran Community of the Dead Sea scrolls, the book of Esther is not among the archaeological finds.
After the persecution of the Christians about 325 CE, the church leaders of the region came together to discuss the issues facing the Christian Church especially the deity-humanity of Jesus Christ in the Council of Nicea. There were already some consensus among the early Church Fathers and bishops which books were considered as Scriptures.
The Council of Carthage in 397 CE came to a conclusion which books were considered Scripture for the New Testament. It is St. Jerome who stated the “Books/Scrolls” of the Bible about 400 CE.
The discussion revolved the authorship of the scroll and its association with the Apostles and Jesus, the dating of the writing, and the consistency of that scroll with the teaching of the other portions of Scriptures.
Christians believe through divine guidance of the Holy Spirit that the 39 Old Testament Books and the 27 New Testament Books are Scripture. Throughout the centuries, Christians questioned some of the other books that were viewed as Scripture by the Catholic Church. Although there is that disagreement beyond the 66 Books, there is no disagreement with the 66 Books.
SUMMARY: The deciding factors by the early Church Fathers for a book to be part of the New Testament were the authorship, dating of the book, and consistency with other Scriptures.
-Kingston