“Men of Israel and you who fear God, listen. 17 The God of this people Israel chose our fathers and made the people great during their stay in the land of Egypt, and with uplifted arm he led them out of it. 18 And for about forty years he put up with  them in the wilderness. 19 And after destroying seven nations in the land of Canaan, he gave them their land as an inheritance. 20 All this took about 450 years. And after that he gave them judges until Samuel the prophet. 21 Then they asked for a king, and God gave them Saul the son of Kish, a man of the tribe of Benjamin, for forty years. 22 And when he had removed him, he raised up David to be their king, of whom he testified and said, ‘I have found in David the son of Jesse a man after my heart, who will do all my will.’ 23 Of this man's offspring God has brought to Israel a Savior, Jesus, as he promised. 24 Before his coming, John had proclaimed a baptism of repentance to all the people of Israel. 25 And as John was finishing his course, he said, ‘What do you suppose that I am? I am not he. No, but behold, after me one is coming, the sandals of whose feet I am not worthy to untie.’ (Acts 13:16-25 (ESV)
So they have made it to Antioch in Pisidia, John Mark has left them for reasons unexplained. But now they are in the synagogue and Paul begins to preach to the Jews, proselytes and those who fear God. What we have here is an example, the general outline of the sermons Paul would give when he came to a new town and first began preaching in a synagogue.
When reading Acts there is always a question of applicability. It records events, but that something has happened one way at one time, doesn’t mean it will always happen that way. So when the Holy Spirit is received by the Samaritans with the laying on of hands as a separate event from baptism, or the house or Cornelius before baptism, this does not mean that the Holy Spirit is always given apart from baptism, or that baptism isn’t the regular means through which one receives the Holy Spirit. In any case, in both those events, baptism occupies center stage. But you get the picture, the recording of an event in one way does not make it normative, it is descriptive, not prescriptive, kind of like a dictionary…. But then sermons do more than record an event, they proclaim God’s word to sinners, Justification by grace through faith. So what is recorded in a sermon is true for all times and all places, especially if an apostle is giving it. A sermon may describe an event, but its purpose is not description but prescription. So what Paul will preach here in this synagogue, is true today too. It is true for you, same as when Peter says that Baptism is for you and for your children in his sermon in chapter 2.
Paul starts his sermons remembering the history of Israel, the whole Old Testament, he ends then with John the Baptist, the last of the prophets of the Old Testament (which is not a collection of books, but circumcision). John then marks the transition from the Old To the New, the beginning of this transition anyway, as the transition is still happening at least as long as the Temple is still standing. For the Jews, much of this would be a review. It may have even been boring. But for the God fearers, these would be those who perhaps have just started listening to Jewish rabbis, hearing about God, but had not yet been circumcised and therefore not part of Israel, this would have been intriguing to them. Here is a God actively participating in the history of this world, actually driving history. Their god’s typically just watched as if they were watching a play, and sometimes would intervene as if the script was a choose your own adventure book. But the God of Israel is active in history, even today. He doesn’t just wind up the watch and let it go, he actively turns the gears. He is operative even in your own life, blessing what you do, working all things good for those who love him. But the chief purpose of Paul recounting the history of Israel is to bring about Jesus, the son of David, the promised one. The story is about Jesus, it is completed and fulfilled in Jesus, and without Jesus it is incomplete, senseless, a collection of gibberish that means nothing. Which sad to say, is the way most read it today, even Christians. Today when we hear the word scriptures, our first thoughts are of the “New Testament” but when Paul used the term he had not in mind the letter to Romans, or Ephesians, or any of the gospels, but he spoke entirely of the Old Testament, Genesis through Malachi, and these testify of Jesus as Paul will show. What Paul writes in his letters is always commentary on the Old Testament in light of Jesus Christ, the savior of the offspring of David, to whom John pointed.