The full title given to the book of Acts is usually “The Acts of the Apostles,” so most divide the structure of Acts using its two major characters, Peter (1-12) and Paul (13 – 28)
But within Peter there is the interruption of a variety of other people.
– Story of Ananias and Sapphira (Although Peter is administrator of the curse, Chapter 5).
– Stephen’s martyrdom (Chapters 6 and 7)
– Phillip (Chapter 8 )
– Saul/Paul (Chapter 8-9)
So at least within the division of Peter there is a lack of focus on Peter.
Thus I’m not convinced this is the best way to outline the book. Surely as a letter of Luke, he had intent as to what Theophilus was to get out of this. I believe it was more than a character study of examples of “good” Christians. What if the focal point was instead, considering the Acts of The Holy Spirit? The people are still important, but they are not the ultimate subject matter, although it is still primarily a narrative. In reading historical narrative (especially from scripture) we should always remember that God is a, if not always the, main character Even when not mentioned. This starting point God in the person of the Holy Spirit becomes the primary one “doing and teaching,” in place of Jesus, in the witness of the Apostles (1:1-2, 4 and 8). What we have then, in the opening of Chapter 1, is not simply the tie-in to the gospel of Luke but (I believe) the proposed structure for reading the rest of the book.
The Apostles are not able to go out on their own; they must wait for the Holy Spirit. Upon receiving the Holy Spirit they will be empowered to spread the gospel geographically outward, starting “in Jerusalem, and in all Judea and Samaria, and to the end of the earth” (1:8). This is fleshed out or fulfilled in the following statements of acts as the appropriate subject divisions.
Acts 6:7 – Then the word of God spread, and the number of the disciples multiplied greatly in Jerusalem, and a great many of the priests were obedient to the faith. (ESV, emphasis mine)
Acts 9:31– Then the churches throughout all Judea, Galilee, and Samaria had peace and were edified. And walking in the fear of the Lord and in the comfort of the Holy Spirit, they were multiplied. (ESV, emphasis mine)
Acts 12:24 – But the word of God grew and multiplied. (ESV)
Acts 19:20 – So the word of the Lord grew mightily and prevailed. (ESV)
Acts 28:31 – preaching the kingdom of God and teaching the things which concern the Lord Jesus Christ with all confidence, no one forbidding him. (ESV)
The last three implying that it has gone out into the ends of the earth, and is still doing so today. It is not a completed act, but a continuing act of the Holy Spirit through the continuance of disciples. So the overarching structure of Acts is the geographic spread of the gospel (and nationalistic, from Jew to Gentile) partnered with the multiplication of the church. Following this structure will reveal the book’s themes along the way. One such common theme is as the message spreads, persecutions follow close behind and yet the church grows, and so it is providentially encouraged to spread more.