Who decided what the canon of Scripture should be and on what basis?
Even before the First Council of Nicaea formally canonized the New Testament, the common belief about which writings were holy scripture was to include things written by eyewitnesses of resurrected Jesus and their close associates. That hasn't changed.
It's amazing that Nicaea (early AD 4th century) was over a century before the first real pope (Leo in mid 5th century) consolidated all the western church's political power under see of Rome (himself) and 7 centuries before pope Gregory defined what we today call "papal authority". Basically, in many ways the church at the time of Nicaea (era of Bible canonization) fell in line with more of what we today call Protestants than what we today call Catholicism. Even the Latin word "catholic" meant universal or encompassing the world (all of God's Christians all over the world), not like Catholics use it today (meaning a subset of Christians).