You do not need to read Luke and Acts together in order to appreciate them. However, they share a similar theme and narrative structure. Both books emphasize the overwhelming and transforming power of the Holy Spirit, first through the healing and teaching of Jesus, and then through his followers spreading his teaching (and sometimes, healing). And both tell how this spiritual authority is directly challenging earthly authorities: in Luke, Jesus brings the Holy Spirit to Jerusalem, the religious center of the world; in Acts, Paul brings it to Rome, the political center of the world.
In Luke, the Holy Spirit empowers all that Jesus does -- his miracles, his teaching, and his acceptance of crucifixion. However, this Holy Spirit is not Jesus' alone -- it works through others too. Through the influence of the Holy Spirit, some people recognize who Jesus is, and the announce this. And through the power of the Holy Spirit, some people go out in Jesus' name, sharing his teaching and healing others. And, beginning with Jesus' resurrection appearances and continuing in Acts, even more people have their eyes opened and lives changed by Jesus.
This divine spirit works in mysterious ways, though, as Jesus tries to explain through his parables and ministry. Everywhere Jesus goes, he completely upends expectations with his words and actions. Religious leaders are frequently not the best religious teachers. Men are not more important than women. Money is not a sign of God's favor or approval. And, perhaps hardest of all, a lifetime of piety does not make someone more important than a convicted thief who believes in Jesus at the last possible moment -- there aren't extra rewards in heaven for some; heaven is the reward for all who are saved.