Antioch was an important city in the first century. It was on the Roman road, and a centre of trade and commerce. When Paul arrived in a city, he firstly went to the synagogue to reach those who he had a burden for.
We find in Acts 13 the first recorded sermon of Paul. To start with, Paul lays an important foundation, that the Lord has raised a savior for Israel, whose name is Jesus. Part of the reason why the Jews were expecting the messiah to provide His Kingdom through a military victory, as David was a successful military king. As the Jews were expecting the messiah to a be introduced by a prophet. And Paul indicates that the prophet was John the Baptist.
In the second section, Paul gives the reasoning as to why Jesus was the promised messiah. As he starts the section, he speaks to both the Jews present and any gentiles who feared God. Christianity is not a discriminating world view. Anyone who calls upon the name of the Lord shall be saved.
Religion is the biggest blight on humanity. Just as the Jews at the time of Jesus did not understand what the prophets were saying, despite reading them every day. And within the realms of Christianity today, we see he same.