Describe the visions of the Federalist Party and the Democratic-Republican Party for the future of the new nations after the birth of the Unites States. How did this contribute in the shape of our current government?

The Democratic-Republican and Federalist Parties had very different visions for the future of the United States. It is often said that the Federalists, led by Alexander Hamilton, envisioned a government and a society not unlike that of Great Britain in the late eighteenth century. Hamilton argued for and implemented policies to establish a powerful central government led by a strong executive and a legislature that was not constrained by the relatively vague language of the Constitution. Essentially, he saw the nation's future in commerce and manufacturing, which he believed should be underwritten by the establishment of a strong fiscal and monetary apparatus at the federal level. Central to this was a national bank that would tie the wealthiest people in the nation to the federal government, and a program that would pay off existing federal debt by taking out new debt in the form of bonds. In this way, Hamilton hoped to encourage the United States to turn to manufacturing for its future and as a means of attaining economic independence.
If Hamilton and the Federalists saw the future of the nation in the manufacturing and financial hubs of the Northeast, the Democratic-Republicans saw it in the West and the South. They envisioned a nation not of factory workers and financiers, but of small, independent yeoman farmers. They argued that many of Hamilton's policies benefited the wealthy over small farmers, and advocated for a strict interpretation of the Constitution. Generally, they favored the French Revolutionaries in the war that broke out between that nation and Britain, who was supported by the Federalists. Overall, these contrasting visions were really simplistic and symbolic in nature. Federalists understood the importance of farming, and Democratic-Republicans did not reject manufacturing as such. Thomas Jefferson did not, for example, dismantle Hamilton's Federalist state when he took over as President in 1801. Rhetorically, however, their arguments would continue to resonate in American politics throughout the nineteenth century and beyond. Democratic-Republicans who opposed a strong national government (when it did not suit their interests) were echoed by conservatives throughout American political history, as were Federalists who argued for strong and robust federal action on issues confronting the nation.
The debates between these two parties reflected some of the differences at the Philadelphia Convention, though the issues of large and small states had mostly become obsolete. They were arguing, in many ways, about the nature of representation itself. To whom would the government of the United States belong? The Democratic-Republicans generally argued that the states should continue to be the source of political power, while the Federalists saw the national government as more suited to handle the challenges the nation faced. These issues still remain today.
http://faculty.polytechnic.org/gfeldmeth/chart.feddr.pdf