1. You may have heard in leadership of the difference between formal and informal power. Formal power is official power, the power of an office. Informal power, though, is much more important and potentially subversive. This is the "church boss," who may not even be on the church board. This is the person in whose direction the eyes turn when a decision is being made... and it may not be the person leading the meeting.
The early church probably did not have too formal of a power structure. There were the apostles, of course. But even then, four "pillars" seem to have emerged as the real leaders among the leaders (cf. Gal. 2:9). At first it was probably Peter, James, and John. These are the names that the biblical texts remember as the core disciples.
But it is not long before James, Jesus' brother, seems to become the real leader of the Jerusalem church. Arguably he became the fourth leg of a four pillared church. Better yet, perhaps these were the four pillars of the new temple.
2. I'll confess that I don't get too excited about the Jerusalem church. I see them as somewhat inwardly focused rather than missional like Stephen and Philip. I see them as conservative such that they easily included Pharisees as believers without much alteration to their previous focus on separation and purity (Acts 15:5). The good news didn't reach the world because of these folk, good though they probably were. God performs miracles, but the Jesus movement arguably would have died if it had been up to them.
3. The church at Antioch was different. It sprung up organically--there were no missionaries sent there officially. Without any approval, they start telling the good news to non-Jews. Although Acts gives its obligatory doff to Peter with Cornelius, my hunch is that the real Gentile mission started here.
Barnabas goes to Antioch to help provide leadership to this burgeoning church. Was it a protectionist move, to help bring order to chaos? It was no doubt a good move, and everything we know about Barnabas suggests he was a great person for the job. Here was a man who was a true statesman, someone who was more interested in the goal than his own status or authority. This was a man who was self-confident enough later to let Paul basically hijack the mission he was in charge of.
In fact, Acts tells us that Barnabas went to get Paul from Tarsus at this point. In one scenario, Paul has been in his home country for over five years. These are his lost years (at least as far as our knowledge of them). Perhaps he had spread the word so zealously that he had burned over Cilicia to the gospel, as he perhaps had in Arabia. Sometimes a person just flips a switch from one zeal to another.
4. The early church had prophets as well as apostles. Ephesians remembers these two groups as the foundations of the early church (Eph. 2:20). Antioch apparently had many of them. They may have had as much to do with the formation of the beliefs and practices of Christianity as the apostles did.
This is the old tension between structure and charisma. Charisma is energetic, wild, and often chaotic, but it has great power. Structure is dependable, long-lasting, and stable, but often boring. In the earliest church, Antioch was the charisma. Jerusalem was the structure.