Again, I would say Peter is giving a sermon and not writing a theological document. By Peter going into detail about the resurrection after speaking of the Christ crucified, that is redemption.
As for receiving the Holy Spirit AFTER baptism we do know there were 120 receiving the Holy Spirit before Peter's sermon. That is why we must look at all of the scriptural evidence. When we go to Acts 10 we see Cornelius and his household hear the Gospel, believe, receive the Holy Spirit and then water baptized. When we go to Acts 15 we see Peter say the following:
6 Now the apostles and elders came together to consider this matter. 7 And when there had been much dispute, Peter rose up and said to them: “Men and brethren, you know that a good while ago God chose among us, that by my mouth the Gentiles should hear the word of the gospel and believe. 8 So God, who knows the heart, acknowledged them by giving them the Holy Spirit, just as He did to us, 9 and made no distinction between us and them, purifying their hearts by faith.
Peter tells all assembled he delivered the same gospel he received and preached it to the Gentiles (Cornelius et. al.) If we look at the sermon given by Peter in Acts 2 and compare it with the sermon in Acts 10, we see little difference. We see the same results.
Any other endeavor to say sometime in Acts Paul instructed Peter on the gospel to preach to Cornelius is just not there. Paul is giving a missionary report in Acts 15 before the Jerusalem council not revealing a new gospel.
If you compared Acts 2 with Acts 10 you would see little difference. Because there isn’t any. Except that Peter was called by a vision to go to Cornelius. Why would he have needed a special vision if he understood the Great Commission correctly? It would have a no-brainer. “Go ye therefore, and teach all nations...” (Matt. 28:19,20). You cannot misunderstand that, no matter how hard you try. “What was I that I could withstand God?” (Acts 11:17)??? WHAT does THAT mean,if they were ALREADY TOLD to go to all nations?? Please, tell me.