The quote "Render unto Caesars what is Caesars, and render unto God what is God's" is referring to tax money. Jesus was pointing out that the money had Ceasar's picture on it so it belonged to Ceaser in the first place.

The context of that statement is that Jesus grew up in the Essene community that did not believe in money. The Essene of Nasareth where Joseph and Mary lived and raised Jesus practiced a communal life style were all the people in the Essene Community shared common stores and wealth. There was no use for money within the Essene community.  Whenever and Essene from one community came to another community they would just seek out the local Essenes and could share their meals and labors.

That is wny Jesus said to not have belongings and to just pick up a staff and sandals and go, because he was advocating the Essene's social gospel community, not the money based community. That is why the money changers in the Temple were so offensive to Jesus.