The story of Jesus is "good news." It is the "gospel" that God has enthroned Jesus as king of the universe. A gospel in the time of the New Testament was extraordinary news, like the birth of a successor to the throne or a key military victory. In the preaching of Jesus, the image of "preaching the gospel" may have pointed directly at Isaiah 52:7 and the good news that God was restoring his people after a time of captivity. 
The sermons of Acts are all encapsulations of the good news as well, and almost all of them climax with the fact that God has raised Jesus from the dead and enthroned him as king of everything.  They are all very similar, which probably shows that they are as much the handiwork of Luke as word-for-word transcripts of exactly what was said on each occasion.  But they nevertheless give us a clear picture of the earliest preaching of the church. 
The sermons of Acts almost all have a roughly similar outline.  First, God had foretold his plan in the prophets of Scripture. He was now making it happen through Jesus of Nazareth. The people of Jerusalem had put him to death, but God had raised him from the dead. The resurrection is the climax of all the sermons in Acts but Stephen's. God installed him as king of everything and has now sent out his Spirit. In response, everyone should repent, be baptized, and they will receive the Holy Spirit...
 See Ken Schenck, Jesus: The Mission (Indianapolis: Wesleyan Publishing House, 2013), 22-23.
 See 1 Corinthians 15:1-8 for another narrative encapsulation of the gospel.
 We know from the Greek historian Thucydides that it was perfectly acceptable for a historian to compose speeches that fit the occasion about which they were writing (cf. History of the Pelopponesian War, 2.97.4). The sermon of Acts 2 gives us a hint of Luke's handiwork in that Peter seems to quote Psalm 16 from the Greek version, while Peter would have spoken Aramaic on the Day of Pentecost. Compare Acts 2:26 with Psalm 16:9.
 A classic here is C. H. Dodd's, According to the Scriptures: The Sub-Structure of New Testament Theology (London: Nisbet, 1952). You can read it for free online here. I studied under Dunn who studied under Moule who studied under Dodd. This basic gospel preaching is sometimes called the "kerygma."
 Arguably Stephen's sermon in Acts 7 would have ended up similarly, but he gets stoned before he finishes.