1. The actual word "gospel" (euangelion) is only used twice in the book of Acts. In Acts 15:7, Peter tells the Jerusalem meeting that God first chose to bring the gospel to the Gentiles through him. This good news was something that they believed. To get a better idea of what this good news was, therefore, we would look at the sermon of Acts 10.
2. The second instance is in Acts 20:24, where Paul says that his ministry is to testify to the "gospel of the grace of God." In this instance, it would be natural to take "grace of God" as the content of the good news. Paul's ministry involved testifying to the good news about the grace of God. Whatever the gospel is, it exemplifies the grace of God in specific ways.
The noun does not occur at all in Luke.
The Verb: "To Preach the Gospel"
The verb form, "to proclaim the good news" (euangelizomai) is probably more helpful in honing in on just want this good news is. The verb appears 15 times in Acts and 10 times in Luke.
1. In one translation of Acts 5:42, Peter and others preach the good news that Jesus is the Christ. This type of good news would fit with the Hellenistic use of the word to announce the birth of a future emperor or a military victory. "Jesus is the Christ" is the announcement that the king has arrived.
2. Acts 8:4 seems to have a similar sense. Philip and others who are scattered preach good news of "the word." What is the word? The next verse suggests the word was as in 5:42. Philip was "preaching the Christ" to the Samaritans. We can presume that the word means the same later in the chapter (8:25).
In 8:35 Philip shares the good news with the Ethiopian eunuch. It is also the good news about Jesus. Then Philip continues to share it in the towns of that area (8:40).
3. In Acts 10:36, the message of good news is "peace through Jesus Christ," who is "Lord of all things." Again, we remember Augustus and the good news of his kingship when he ushered in the pax Romana ("Roman peace").
What is nice about Acts 10 here is that Peter goes on to give the details of what this good news of the Christ is (and remember that 15:7 pointed us back to this passage in reference to what the gospel was). The gospel was the word that was proclaimed throughout Judea. It involved a story that started with John the Baptist.
The story involved casting out demons. But the preaching about him was that he was ordained to be the judge of the living and the dead (10:42). In other words, the good news centers on his kingship. However, it also involves the possibility of forgiveness for sins (10:43).
4. Acts 11:40 - They preached the Lord Jesus (Jesus is Lord, Jesus is king again).
- Acts 13:32 - The good news promised is that Jesus is God's Son (13:33), his king.
- Acts 14:7 - Doesn't give contextual clues about what they're preaching but presumably the same.
- Acts 14:21 - No specifics mentioned, but the message elicits disciples or followers, which we would expect of a king.
- Acts 15:35 - Paul and Barnabas continue to preach the good news at Antioch. The good news is the "word of the Lord" (cf. 8:25). Since Lord relates to Jesus as king, it fits again that the center of the good news is the enthronement of Jesus as king.
- Acts 16:10 - no specific content given
7. As far as the Gospel of Luke is concerned. Luke 1:19 indicates that the coming ministry of John the Baptist can be good news. The birth of Jesus the Savior is good news in 2:10 (cf. Augustus). John the Baptist preaches the good news of Jesus' arrival in 3:18.
Jesus preaches the good news of the arrival of the kingdom of God (4:43; cf. 8:1; 9:6; 16:16; 20:1) and predicts its demonstrating in his healing ministry (4:18; cf. 7:22).
The good news in Acts centers on the inauguration of Jesus' kingship, with all that it entails. There is continuity between the good news of Jesus reign and the good news in Luke of the arrival of the kingdom of God, for Jesus is the king God is installing. Entailed in that kingship is of course the peace of his reign, forgiveness of sins, the judgment of God's enemies.