I Baptize Thee, William Johnson, 1940
Smithsonian American Art Museum
Read Acts 10:44-48
When Jesus was baptized, as he was coming up out of the water, the Spirit descended on him like a dove. (Matthew 3:13-17) First baptism, then the Spirit.
In this passage from Acts, the Spirit fell on the listeners as Peter was preaching. The people began speaking in tongues and exalting God. Peter realized that he could not withhold the water of baptism from those who had received the Spirit, so he ordered that everyone be baptized in the name of Jesus Christ. First, the preaching, then the Spirit and its manifestations, and then the water of baptism.
Both stories (and additional variations) hold a place in the New Testament. The administration of baptism and reception of the Holy Spirit are common to those stories; but the stories tell of differing experiences by different people.
I don't believe that there is a prescribed order by which these things must take place. After all, we are talking about gifts of God's grace. They cannot be reduced to a formula. God works in each of our lives differently.
The more important question is whether we are living out our experiences of baptism and of God's Spirit in a way that is consistent with our new identity and the expectations of Jesus Christ.