For I have chosen him, that he may command his children and his household after him to keep the way of the Lord by doing righteousness and justice, so that the Lord may bring to Abraham what he has promised him.
The personal elements of the covenant are interesting to see in this passage. God did the choosing of Abraham. There was no merit on Abraham's part to earn the "right" to receive the covenant. It was God's choosing of him that gave him the covenant. But there was responsibility in the covenant. Abraham was to begin a dynasty of faithful obedience and walking with God. He was to command his children and household to follow God and to doing what the Lord said was righteous and just.
The result of the choice and of the obedience was that the covenant would be honored by God. He would bring Abraham what He had promised. This personal relationship with God just keeps being explained and exemplified in the life of Abraham.
What is really interesting in this passage is that Abraham, through the normal practice of hospitality, winds up entertaining God, Who gives him further insight into the events that would transpire. Once again, Isaac is predicted to enter Abraham's household. It is clear that God will continue to honor the covenant through this child of promise. God is clearly doing the heavy lifting in the covenant. Abraham is just remaining faithful and obedient.