At the time of Jesus birth caves were sometimes used as stables. The manger which held our Lord Jesus wouldn't have been very pretty. Animals ate out of it. This was the Lord's humble entrance into our world.
Matthew was a Jew and a tax collector for the Romans. Luke was a Greek physician. Most Greeks and Romans had no respect for anything Jewish. Luke was probably an exception to this and Matthew might have had a better understanding of the scriptures because he already understood the perspective they were written from. The Lord used those who made themselves available to spread the gospel, the same as He continues to do today.