To understand fully what God has done, it is necessary to go back to the beginning to see His purposes in choosing Israel. Israel's beginning occurs, not with Jacob, but with the calling of Abraham.
God's final remark in verse 3 is the most fundamental reason God chose Abraham, and thus Israel and his descendants: to bless mankind in the Person of Jesus Christ. Christ is the center, the focus, of everything. He is the end or the goal of the law (Romans 10:4), the One toward whom the whole Old Testament was written (Galatians 3:24; see Luke 24:44). As Paul puts it, to us He "is all and in all" (Colossians 3:11; see Ephesians 1:23).
Physically, Jesus had to descend from some line of humanity. Abraham, who was himself descended from those who had been faithful to God in earlier times, possessed special qualities that pleased Him. Therefore, He chose Abraham and his family, which later became known as Israel, to work through to bring the wonderful blessing of salvation to all mankind. God says of him:
For I have known him, in order that he may command his children and his household after him, that they keep the way of the LORD, to do righteousness and justice, that the LORD may bring to Abraham what He has spoken to him. (Genesis 18:19)
This man had a special relationship with God: He knew God, and God knew him. God says He had worked with Abraham to bring out the qualities that would allow the patriarch to command his descendants so that they would keep the way of the Lord. In other words, Abraham had such a force of godly character that he would pass down to his descendants an affinity for God's way (see the principle in Exodus 20:6). In Abraham, God created a people who had a special link to Him. God knew that, for the purpose He was working out, Abraham was the best candidate, later called "the father of us all" in the faith (Romans 4:16), from whom to build a model nation with certain desired qualities.
We should be careful not to take this idea too far. Abraham was not perfect; he sinned and his story reveals that he had to grow a great deal. Nevertheless, he was the only person whom God ever asked to sacrifice his only son, just as He did. If nothing else, this puts him at least one rung above the rest of us. Beyond that, his righteousness does not make his descendants one whit better than other people of the earth. Their prime advantage lies in the fact that, since God had a close relationship with Abraham, they hold a special place in God's heart (see Deuteronomy 7:7-8).
This is the beginning of Israel. For His purposes, and to produce an eventual blessing for all nations, God started with the best clay that He could mold.