Anyone wanting detailed application of this long passage following my last post is going to be disappointed. There just isn't the space in a blog post. Go do it for yourself. These are just a few observations:

I think we are meant to read this as an example or model evangelistic sermon, at least for the Jewish context of the first missionary journey. It is Luke telling Theophilus and us "this is how we did it - this is how it is done." He started Acts 13 telling us how the Holy Spirit set people aside for the work. Then he showed us that when he does we get confrontations between God and Satan with Jesus destroying the power of the evil and bringing life and immortality to light through the gospel. Now he is showing us an example of the kind of message about Jesus that was delivered. He doesn't go into detail in the other locations in chapter 14, this is his model of how it was generally done.
Paul recapitulated God's well-known saving acts in history. He picks examples that show that God rescued despite his people's sin not because of their worth. In other words he shows that God always acted to rescue because of his grace.
The repeated need for God to come and rescue demonstrates that none of the Old Testament rescues were final. They always anticipated something greater. Finally John the Baptist came preaching repentance and baptism for the forgiveness of sins, saying one was about to come who was greater. The point being that they knew from their history and from John that God would act in a greater and more decisive way than they had seen before.
This greater rescue was that he raised Jesus from the dead after he had been the victim of the sin of people. He is thereby proved to be greater than David (v36)
The conclusion and application of the message - the whole point of preaching - is v38-39. Paul says we can now be justified from everything that could not be justified by the Law of Moses. It is a VITAL point. Let anyone who thinks that Christians now relate to God through the Spirit being given to help us obey the Law of Moses take note - there were things that it never justified. It is now fulfilled and superseded by the forgiveness of sins in Jesus. This is the point of all evangelistic preaching. We don't do it to Gentiles in the same way as to Jews, but the goal is the same - turn to Jesus not religion (or anything else) to get your sins forgiven
To underline the point, when many turned to the Lord the apostles encouraged and urged them to continue in grace (v43)
The next week the whole city turned out, but so did abusive and jealous people. Paul and Barnabas say a very interesting thing to them: "since you do not consider yourselves worthy of eternal life we now turn to the Gentiles." In other words getting eternal life is inextricably linked to receiving grace and forgiveness of sins (very similar to Romans 5:17)
When they go to the Gentiles, the Gentiles were glad and honoured the word of God. All who were appointed for eternal life believed. Note the connection:
1. Jesus forgives sins, thereby justifying what could not be justified by the Law of Moses;
2. Receiving this grace and forgiveness from God gives eternal life;
3. Those who get eternal life do so by believing the message. That is, if you believe and receive the message of Jesus, God gives these gifts to you
A riot ensues, the mission team are run out of town. AND the disciples were filled with joy and the Holy Spirit. Here is the normal pattern for what happens when the church of God preaches the message of God in the power of God to a world that hates God. Society reviles, oppresses and opposes. And people are saved, filled with overwhelming joy and given the abundant gift of the Holy Spirit. Hallelujah.