In those days Israel had no king; everyone did as they saw fit. (Judges 21:25)
Does the Old Testament give us an ideal or perfect form of government to strive for? Yes and No.
If we look at the form of government that existed prior to the flood, the Scriptures are not very descriptive of what governance there was. There had to be some, but we are only told what God added to the scope of human governance in Genesis 9. Here He introduces the concept of capital punishment for those who take human life. When Cain killed Abel he was not killed but God marked him and exiled him. However, now, those who kill another will be killed by the state.
In other words, it seems God tailors the form of government to the extent of mankind’s evil. No government is perfect or ideal because human rebelliousness makes it all for naught. When Israel is confederated as a nation they enter Canaan as a loose union of tribes with their own leadership structure (elders and judges). The Judges rule over their various scopes of influence (a tribe or two) but not the whole nation. The author of Judges makes a point that there was no king in those days and that everyone did what was right in his own eyes.
When the people ask Samuel to give them a king and reject him as judge (1 Samuel 8), Samuel and God both characterize their request as a desire to get out from under God’s rule:
But when they said, “Give us a king to lead us,” this displeased Samuel; so he prayed to the LORD. And the LORD told him: “Listen to all that the people are saying to you; it is not you they have rejected, but they have rejected me as their king. As they have done from the day I brought them up out of Egypt until this day, forsaking me and serving other gods, so they are doing to you. Now listen to them; but warn them solemnly and let them know what the king who will reign over them will claim as his rights.” (1 Samuel 8:6-9)
Nevertheless, God gives them a king and all predictions of the coming Messiah now make him out as the one who will rule on the throne of his father David. Deuteronomy 12 even anticipates this, though it was written before Israel conquered Canaan and gave up the governance by judges.
So if there is a perfect form of government (and there isn’t because there is no perfect human group to governed as yet), it is that government that best keeps in check human sinfulness. The only reason the American form of government has worked as successfully as it has is because our founding fathers took seriously the depravity of humans and built checks on human abuse of power into our system. Even these have not been enough to prevent all such abuse. The human heart is also sneeky and finds ways to corrupt the best of governments.
One day Jesus will rule over all the world and his governing will be perfect, the servant leader who rules in righteousness and is never corrupted by power. But even in his kingdom, in its early stages, that is, he will have rebellious subjects who will try to overthrow Him in a coup (Revelation 20). They will fail. Not until humankind’s sin is totally eradicated by the resurrection will be able to be fully governed in righteousness.