I believe that Luke's purpose(s) for writing Acts was to assure that we know the whole and complete truth regarding the truth we were taught by those before us. We are told that many individuals before us have done their best to write about the accounts of things that had taken place before/among them at the time. Luke doesn't insist to say that these truths were ineffective, but instead, he wants to write a report that he believes would make things a little clearer for us, ensuring our beliefs in the truth that was given to us prior to this. These were individuals who were servants of God and who were spreading the word since the start of the message given by Christ himself. He himself has done some studying on his own. He mentions that his studies were that of their "beginnings," therefore he insists that he writes an orderly account for us, helping us to better understand the truths from their beginnings as well. He mentions it as being "good." Therefore, the birth of John the Baptist, the birth of Jesus, etc, each play a major role in Christian truth but are better understood in an orderly fashion. Knowing these truths and their importance from the start until the end of Jesus' life, as well as what to come, Luke believes is significant. Again, stating that we would then have the "full" truth about everything we have learned and have been taught. That is why he addresses this letter to Theophilus. Many individuals who read the book of Luke without paying much attention to that name tend to assume that Theophilus is a person, more concretely a man, although, after careful study, I have understood that Theophilus is not one being, but instead a general term. Moreso, a general term referring to those who believe in Jesus Christ. The term Theophilus is also another term for Christian, or lover of God. After digging a little deeper, I have also concluded that Luke had probably even dedicated both of his gospels (Luke and Acts) to a Roman. I found this to be interesting due to the fact that Luke calls himself "most excellent," a name/title Paul uses in addressing Felix and Festus later on in the book of Acts. Because of this, many have concluded that Theophilus could even be a person of rank, perhaps a Roman official.
According to Acts 1:8, we can see that the Gospel had moved on an accordingly basis. What I mean by this is that Jesus had a plan and a certain way in which he wanted his gospel to be spread. The spreading of the gospel was/is a big deal. Therefore, the disciples needed to be ready for this responsibility. We see this, because according to Luke: 24:49, where Jesus tells the disciples to wait in Jerusalem until they receive the Holy Spirit. Many have read this verse and have overlooked its importance. They merely see that Jesus is leaving, and because he is leaving he is sending his holy spirit. This is true, but there is much more to it than that. "And now I will send the Holy Spirit, just as my father promised. But stay here...