Why did God write the Ten Commandments with His own finger on stone? And why did He allow Moses to write the ceremonial laws on paper scrolls?
Peter instructed Christians, "Whoever speaks, let him speak, as it were, the utterances of God." (I Peter 4:11) As a teacher of God's word, I am restricted to teach only the things revealed by God. Not everything has been revealed to us. Moses told the Israelites, "The secret things belong to the LORD our God, but the things revealed belong to us and to our sons forever, that we may observe all the words of this law." (Deuteronomy 29:29) What God has revealed is important for our obedience to God and His law. The Spirit has revealed many hidden things from God and we recognize that these are the wisdom of God and not man (I Corinthians 2:10-13).
It is a fact that the commandments were written on tablets of stone by the very finger of God (Exodus 31:18). These were destroyed by Moses when he discovered the Israelites worshiping idols. God later commanded Moses to make a second set (Exodus 34:1-4). This set was also written by God (Deuteronomy 10:1-4). The words written on these tablets were the ones God first spoke directly to the Israelites (Deuteronomy 5:4-5). These tablets were placed into ark of the covenant, where no man was allowed to look.
Moses was also commanded to write out the law (Exodus 24:3-8, Deuteronomy 31:24-26). These were to serve as a judge against the people, to show their inability to keep God's law. To ensure that it was followed, the king was to make his own personal copy (Deuteronomy 17:18-20). Notice that it was the written words of Moses that would judge the people because those were the words to which they had access. While the people knew what was written on the tablets of stone, those tablets were inaccessible.
Paul uses the medium on which the Ten Commandments were written to show the difference between the old and new laws. "Being manifested that you are a letter of Christ, cared for by us, written not with ink but with the Spirit of the living God, not on tablets of stone but on tablets of human hearts. Such confidence we have through Christ toward God. Not that we are adequate in ourselves to consider anything as coming from ourselves, but our adequacy is from God, who also made us adequate as servants of a new covenant, not of the letter but of the Spirit; for the letter kills, but the Spirit gives life. But if the ministry of death, in letters engraved on stones, came with glory, so that the sons of Israel could not look intently at the face of Moses because of the glory of his face, fading as it was, how will the ministry of the Spirit fail to be even more with glory?" (II Corinthians 3:3-8) Notice that Paul states that the covenant has changed. There is now a new, more glorious covenant written on the hearts of Christians.
Yet, you asked why God chose various mediums (voice, stone, paper) to express His words. While I might hazard guesses, God has not revealed His reasoning within the Scriptures. Hence, I too must remain silent.
You called the law written on paper "the ceremonial law." Such a phrase doesn't not appear in God's Holy Word. He did not divide His law into a ceremonial and non-ceremonial portions. To do what God has not done would violate His teachings.
Notice that when Jesus was asked what was needed to inherit eternal life,
two laws are quoted (Luke 10:25-28). Neither law appears in the Ten Commandment
written on stone. They are a part of Moses' writings. These were what
a man needed to live under the Old Law.