When I say theocratic commune, I’m capturing two independent things: theocracy and communism. The first government that God created was a theocracy. He chose Moses as the leader of His people. Moses, apparently with God’s approval, took Jethro’s advice to create a hierarchical theocracy where the the various levels of the hierarchy were directly chosen by God’s appointed, Moses (Ex 18). When Moses died, he was replaced by his chosen successor, Joshua. Again, this appears to be within God’s intent. So we here we have what appears to be God’s model: a single individual, picked by God, leads God’s people and selects his subordinates and successor.
After the death of Joshua, the Israelites fell away from God, but we get to see God repeat Himself by selecting Judges to lead the people. In some cases the people do not follow the Judges, but God’s intent seems clear: He will select the initial leader for His people, and if possible that leader will select a successor. (The hand-picking by God can also be seen in the Kings, but I won’t belabor the point.)
This is picked up in Acts and the early Church. The key to authority was your theological lineage. I was taught by someone who was taught by Peter who was taught by Christ, therefore my words have more authority than someone who was taught more indirectly. Whether you accept Apostolic Succession or not, this is a key point. The early Church only accepted the various witnesses because they could claim a lineage back to an eyewitness, and even most Protestant churches rely on this claim (see Reinventing Jesus for a modern apologetic example, and my bookshelf for a short review of it). While Paul is a rather startling exception to this rule, he was clearly accepted as an true eyewitness to the post-resurrection Christ, and as the primary evangelist to the Gentiles, one can see him as becoming the new prime-locus rather than the Apostles (this can be seen in the Paul-centricity of the New Testament outside the Gospels, including the later parts of Acts).
In any case this wild tangent is primarily intended to point to the continuation by the early Church of God’s “I pick the first leader, then he will pick his successor if all goes well” model. This is roughly the model that the Roman Catholic and Orthodox Churches follow, with a claimed lineage back to Peter, and seems the most consistent with God’s previous systems (though a more Biblical system might have the Pope rather than the Cardinals choose the next Pope, at least in the Roman Catholic case). I’m not going to get into the question here of whether the Latin or Eastern Church has greater claim to this legacy. My point is their ongoing mechanism for choosing their leadership, not whether they have done so accurately at each stage.
As a small side note, it’s worth mentioning that the Church in Acts also had a mechanism for determining the will of God when it was not clear. They cast lots (Acts 1:26). Casting of lots is a long-used practice for divining the will of God in the Old Testament. So it’s no surprise that this would be part of the decision making process for the Biblical Church.
So that’s Theocracy more or less, and it’s what the Bible prescribes for God’s people. Let’s look at Lukean (Book of Acts) communism for a moment. It’s hard to be more clear than Acts 4:32-34:
32 All the believers were one in heart and mind. No one claimed that any of his possessions was his own, but they shared everything they had. 33 With great power the apostles continued to testify to the resurrection of the Lord Jesus, and much grace was upon them all. 34 There were no needy persons among them. For from time to time those who owned lands or houses sold them, brought the money from the sales 35 and put it at the apostles’ feet, and it was distributed to anyone as he had need.
Acts 5 is even more explicit and includes the death to those who would hold back money from the Church/commune. Yes, I know of the interpreters that say it was because Ananias lied, not because he held back the money, but I think this is a purposeful misreading of the text. The only reason Ananias lied is because the expected behavior was to give all of your money to the Church (4:32, 5:4). The point is that once Ananias had “disposal” of the money, he was wrong to keep it for himself. Only when it was locked up in land was it considered apart from the Church’s assets.
Other verses are important here, such as 2 Thess 3:10 (“If a man will not work, he shall not eat”), and Acts 6:1-4 which explains how to set up Deacons (those who would take care of the day-to-day running of the Church). But really, Acts 4-5 lays out unambiguously what a proper Church should look like, and that is as a commune.