I don't consider
Acts 1:16-23 to be a sermon or teaching but something spoken by the Apostle Peter in a business meeting.
I believe
Acts 2:38-39 is a call to salvation and also to post salvation experiences for Christians such as baptism in water and baptism in the Spirit.
Peter told the crowd on that Pentecost Sunday back in AD 30 how to get saved in
Acts 2:21 when he said that whoseover calls on the name of the Lord shall be saved. The "plan of salvation" preached by Peter and Paul is the same i.e. call on the name of the Lord.
As Peter brought his sermon to a close, many were convicted and cried out, "Men and brethren, what shall we do?" (not what shall we do to be saved as it is often misquoted). That is recorded in verse 37.
Peter then said:
1. turn to the Lord in repentance, call on Him for mercy and be saved
2. Follow up that salvation experience with the mikveh/baptism ceremony because of the forgiveness/remission of your sins
3. And you too can receive the Promise of the Father, this great Holy Ghost Baptism experience which Jesus has poured out on us.