From Acts of the Apostles, by William S. Kurz, SJ, commenting on Acts 10:34-38
Skipping Jesus’ infancy (Luke 1–2), Peter focuses on Jesus’ public life beginning in Galilee after the baptism that John preached. Peter uses a shorthand expression that combines John’s preaching of repentance with his ritual act of baptizing people, which together were an indispensable preparation and catalyst for the public ministry of the Messiah. John’s baptism of Jesus, when the Father affirmed him as his beloved Son, was at the beginning of Jesus’ public ministry (Luke 3:21–22).
Like Luke’s Gospel (3:22; 4:1), Peter emphasizes that God anointed Jesus . . . with the holy Spirit and power. Although the Spirit was with Jesus from his conception (Luke 1:35), at his baptism the Spirit empowered Jesus’ human nature for his ministry of preaching, healing, and exorcisms, just as the Spirit empowers the Church for ministry in Acts.
Fortified by the Spirit and divine power, Jesus went about doing good and healing all those oppressed by the devil. Peter’s explanation that God was with him emphasizes the presence of the Triune God with and in Jesus’ humanity. Luke’s emphasis on Jesus’ humanity— rather than on his divinity, which John’s Gospel more frequently accentuates— shows that Jesus worked miracles not only as God, as stressed in John, but also as a Spirit-empowered man, who is therefore a model for all his disciples.
This enables Luke and Acts to underline the continuity between wonder-working prophets like Moses and Elijah, the miraculous prophetic ministry of Jesus, and the miracles of his Spirit-empowered followers like Peter, Stephen, and Paul in Acts. Peter and others imitated Jesus’ healings as part of their prophetic witness to God’s saving message; so such works are likewise possible for Spirit-empowered Christian readers of Luke-Acts.