Paul is Gods’ chosen apostle to the Gentiles, so he writes to Gentiles only (he writes to Jews in Hebrews). It is Paul alone that speaks of salvation by grace through faith
Paul is not writing to Gentiles only. He is writing to both Jew and Gentile who are now Christians. Romans is the most obvious. We can identify several in Pauls letters who are Jews. Timothy was half Jew. Priscilla and Aquila were Jews. Many others.
When studying scripture, one should always ask: Who is speaking or writing? To whom are they speaking or writing? and What are the circumstances?
Let's take your advice. In 2 Timothy 2:15 Paul is writing to Timothy (The Who) The circumstances are Paul is giving Timothy instructions on ministry. When Timothy received that letter the only scriptures Timothy could "rightly divide" is the Old Testament and his letters. Timothy did not have the New Testament. We must ask ourselves what was Timothy to rightly divide.
Getting back to the Great Commission, Jesus is talking to the apostles, not all Jews in general. By the way…Jesus even stated that He has come to save the lost sheep of Israel…not Gentiles.
Matthew 15:24 (KJV)
24 But he answered and said, I am not sent but unto the lost sheep of the house of Israel.
Jesus only went to 2.5 Gentiles in his ministry – the Canaanite woman in Matthew 15, the Roman Centurion in Matthew 8, and the Samaritan woman (half Gentile) at the well in John 4.
Most, if not all Christian churches today believe that each and every one of us are to be missionaries and quote the Great Commission. But Paul states clearly that we do not all have the same calling:
Again taking your advise on understanding The Who, When and circumstances. We must remember that the mystery had not been reveled during the period before the cross. Of course Jesus instructed the Apostles to go only to the Jews. God's grace and salvation plan to the Gentiles had not been reveled by God YET. We cannot assume that post the revelation the 12 Apostles continued to take the message to the Jews only. Ephesians 3 tells us that the mystery was reveled not only to Paul but to the Holy Apostles and Prophets by the Holy Spirit. So that clearly means that many had knowledge of the mystery, possibly at the very same time Paul was given this knowledge. I believe the revelation was responsible for the transition nature of the book of Acts. We know that some in the Church in of Corinth claim to follow Peter (Cephas) 1 Corinthians 1:12-13
I agree that before the cross the message of salvation was much different and only for the Jews. I do not think we can say that the commission continued that way post the cross and after the Holy Spirit reveled the mystery to the other Apostles. I believe the light came on in Peters head first due to his experience with Cornelius.
I think the most important thing to divide in the scriptures is not Old Testament from New Testament but Before the Cross and After the Cross.