The most common term for Protestant thinking about the ultimate goal of human life is the Kingdom of God. This is Jesus' term in the gospels for the establishment of God's reign on earth, evidenced in perfect harmony with God's will and in perfected human communities. The debate among Protestants is about when this Kingdom will be fully experienced—now in part? only at the end of the ages?—and how it will come to be—only by God's direct action in some future time, say through the return of Jesus Christ? in and through human efforts?
The earliest Protestant reformers believed they were living in the end times and that their reform of the Church would play a role in the imminent return of Christ. They expected human governments to keep sin in check enough to make possible the preaching of the Gospel, but they did not expect radical improvement in human societies.
John Calvin certainly did not expect a progressive spiral of history leading to some sort of utopia on earth. Humans would remain in an imperfect and fallen state until the end times. But Calvin's actions in Geneva clearly show that he also did not think human society would necessarily be some sort of chaotic dystopia. The church in Geneva was run by a consistory, which was a body that included both clergy and lay people (elders). One of the roles of the consistory was to advise the city council on how to make Geneva as just and godly a city as possible. Calvin advised the city council to regulate dress, parties, and the use of makeup by women. (The rigor of the "godly" standards of behavior for all Genevans is likely one cause for Calvin's expulsion from the city between 1538 and 1541.)
Calvin's cautiously optimistic prospects for society are based on his belief that, in order for God's providential plan to unfold, and for the elect to be saved, society must be functional enough for the Gospel to be preached and the sacraments to be celebrated. To facilitate enough social order for this to occur, part of God's grace was to send governments that, while never perfect and often very unjust, kept human depravity in check. Even the non-elect were endowed with conscience and will to live a (relatively) moral life.
Some Anabaptists have believed that one of the duties of the Church is to model for the rest of society what the Kingdom of God is like, thus they have historically been less likely to cooperate with what they perceive to be a fallen society. In a most extreme understanding, like the Amish, they separate entirely, rejecting the norms of an ungodly world. Others might resist the pressures of government as conscientious objectors, refusing to vote or take oaths in a court of law, etc.
During the 19th century many American Protestants interpreted the singular reference in the Book of Revelation to a thousand-year (millennial) reign of Christ in such a way that they believed that Christ would return to rule on earth before the saved are gathered into heaven. This interpretation is called "post-millennialism," literally "after the millennium." The task of Christians then was to prepare for this coming of the Kingdom of God by making the earth a worthy place for Christ's return. This led to times in the history of Protestant churches when they have been slightly more optimistic about the prospects and purpose of building a good society. For instance, many of the reforms of the Progressive Era in the United States (1890s to 1920s) were led or undertaken with great participation by Presbyterians. Such reforms included temperance, women's suffrage, prison reform, and educational reform. Perhaps the culmination of Presbyterian Progressive energies came in the Presbyterian Woodrow Wilson (1856-1924), who, as President of the United States, entered World War I in part because he believed a victory over Germany could end all wars. He also invested great effort in the founding of the League of Nations. (Though he did not succeed in getting the United States Senate to ratify it, the League was a forerunner of the United Nations, established after World War II.) He believed that an international body dedicated to dialogue and diplomacy could greatly improve international cooperation.
One writer on the possibilities for society from the Reformed tradition who remained perhaps closer to Calvin's thought was Reinhold Niebuhr (1892-1971), who grew up German Reformed. Niebuhr's view of society was informed by a Calvinistic view of human nature as sinful at its core, and thus the real possibilities of establishing a perfect human society were very limited. In his classic work Moral Man and Immoral Society (1932) he argues that even when individuals act selflessly, their actions are almost always in the service of a group that is acting selfishly. This is true of nations, classes, and races. His blueprint for creating a "just enough" society (a truly just society was humanly impossible) through the practice of non-violent resistance was influential on the civil rights movement. His tone of cautious optimism (we can and should do better, but we will never do very well) recapitulates the tone of Calvin's efforts in Geneva.