Kingdom in Scripture

The Bible speaks of the kingdom of God in various ways, including those you've mentioned. It is probably also worth mentioning that in some sense the kingdom of God was already here on earth even in the Old Testament. Just as the church represents that kingdom now, Israel did so in the past. Consider, for example, that God was Israel's first king (1 Sam. 8:7), and that the Davidic kingship corresponded to God's kingship over Israel (1 Chr. 29:23). The coming of Christ inaugurated the restoration of the kingdom, the phase of the kingdom in which God manifests his rule over all the earth rather than limits it to the nation of Israel. The Old Testament pointed to this worldwide conquest in a few ways: God promised Abraham that "all nations" would be blessed in him; the prophets frequently prophesied about the nations worshiping God in the future; the prophets also indicated that on the Day of the Lord, God would wipe out all his enemies and establish his reign over the whole earth.

Nonbelievers will never obey God (Rom. 8:5-8). At the second coming, the wicked will be judged and destroyed. Everyone who is left (i.e. believers) will obey God perfectly.

The Old Testament does not distinguish between the persons of the Trinity in any way that can be determined with confidence. Basically we rely on the New Testament's understanding of the Old Testament to figure out how Jesus and the Father are related in this reign. In the New Testament, we learn that Jesus is at the right hand of the father, meaning that Jesus is the main one in charge under the Father (Heb. 1:3; etc.). Paul confirms this idea in 1 Corinthians 15:24-28 where he says that Christ reigns over everything except the Father, and that he will eventually turn over his reign to the Father. Then there is the added difficulty of the correspondence between the Davidic throne and God's earthly kingdom: Jesus did not become heir to the Davidic throne until the incarnation. In that sense, we can't say that he was reigning over the Davidic throne during the Old Testament period. One these bases, I would suggest that it is better to see the Father reigning in the Old Testament.

When did Jesus begin his reign? That's a good question. The Bible seems to speak of this both as a present reality (John 18:36) and a future expectation (Mark 14:25; Luke 23:42) during the time of Jesus' ministry. Certainly he was heir to the kingdom at his birth, and in his death he was the covenant representative of his people, implying that he was their king. But I'm not sure we can put our finger on the precise moment when Jesus became king. This isn't really so strange, though. Consider David: When did he become king? When he was anointed? When God gave him the throne? When some called him king? When Saul finally died? When he officially took control of Jerusalem? I'm not sure the biblical authors thought about becoming king in the same way that we do. We tend to consider someone a king upon his official coronation, but I don't think it is that cut and dry in the Bible.

Right now, the kingdom is present wherever God manifests his authority on earth, from individual believers to the church to institutions or even nations. Primarily, the visible church is the kingdom of God, just as Israel was God's kingdom in the Old Testament. The kingdom includes both believers and unbelievers (e.g. "tares and wheat"), though the whole corporate organization is in submission to Christ.