Why was the synagogue a logical place for Paul to start his ministry?
The synagogue was a logical starting point because Israel had been God's covenant people, were steeped in the Word of God, and were the very writers of this Book. Paul went to the Jew first, as Romans 1 declares, before turning to Gentiles after Israel's rejection.
Les explains that as Paul began his earthly ministry in Acts, every place he went he went first to the synagogue of the Jew. It was logical because Israel had been the covenant people of God, steeped in the Word of God, and the very writers of the Book. After about 30 some years of continued rejection, Paul said, from henceforth we go to the Gentiles, because Israel as a nation was rejecting it. For the last 1900 and some years the Gospel has gone primarily to the Gentiles, but it is still open to a Jew who comes the same way, since there is no difference.