Perhaps the main disagreement concerning polity is whether or not the Bible
prescribes a polity. To some degree, the prime defenders of a particular polity as *the* biblical church government are Confessional Presbyterians, and I'm not simply saying this because it happens to be my conviction. Presbyterians (by name!) demonstrate their peculiar, jus divinum (divine right) understanding of the place of polity in church-life.
Lutherans are historically pragmatic. Anglicans follow the hierarchical model inherited from Rome, and defend it primarily from the traditional angle, considering it the expedient and wise judgment of the church.
Congregationalists, insofar as they follow the Presbyterian model, generally seek biblical precedent; however the thrust of congregationalism is
via negativa, by which the least amount of governance is affirmed. Congregationalism does not have a significant need for what I would term a
positive, highly
developed doctrine of church government. The locus of power is in the individual and the aggregate individuals (democracy). These elect and depose leaders, according to more or less biblical criteria, depending on the church.
Because congregationalism is almost exclusively interested in the
limitation of church-power, by its very nature there is not much need for arguments beyond appeals to the
fact and
character of leadership as things found in the Bible, or in history. The practical reality, then, of congregational churches shows itself in different ways that such churches will be "like" various connectional type churches at their congregational-level. The congregationalist church will be like presbyterianism in some things, or like episcopacy in other ways.
I'm not saying that there exists no books, articles, or essays that give a reasoned or biblical defense of congregationalism or of episcopacy. But in the nature of the case, the episcopal type make more of pragmatic arguments, and the congregational make more of negative arguments (to oppose the episcopal claims, and to oppose the presbyterians for half-measures).
The Reformation of the church, generally, brought into focus the question of church-government. Papal abuses demanded it, and it was Luther who self-described his eye-opening realization that the pope could not be appealed to for a solution to the doctrinal problems, because the papacy was the root of (many) problems. The strict, hierarchical form of church-government had been adopted across the ancient Roman world, in increasing measure over the centuries (especially from the 2nd to the 6th), as secular, Empirical authority was aped; as apostolic-institution was superseded by, and reinterpreted along, man-made politics.
For general discussion of the issues, and biblical defense of the Presbyterian conviction, I recommend:
1) Thomas iWtherow, "The Apostolic Church: Which Is It?"
Which is the apostolic church?: An inquiry at the oracles of God as to ... - Thomas Witherow - Google Books
2) Douglas Bannerman, "The Scripture Doctrine of the Church"
The Scripture doctrine of the church - David Douglas Bannerman - Google Books