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?

Following the Independence of the United States, two major political parties emerged in the new country. Federalists, led by individuals like Alexander Hamilton and John Adams, hoped to establish a more powerful federal government. They had noted the failure of the nation's first constitution, the Articles of Confederation, and hoped that the new Constitution would address those issues. The Articles of Confederation left the United States federal government without a president, national court system, ability to settle disputes between states or regulate interstate commerce, and largely without an army. The Federalist vision of the United States hoped to see a federal government that addressed those issues.
Federalists also typically believed in a loose interpretation of the Constitution that allowed the federal government to do more than what was specifically stated in the Constitution. An example of this would be the creation of the National Bank. The "Necessary and Proper Clause" of the Constitution was cited by Federalists as giving the federal government the power to do more than what was specifically stated, such as the creation of a national bank. Federalists also tended to view the future of the United States as being focused around manufacturing (as opposed to agriculture), shipping, and closer relations with Great Britain. Federalists also favored the idea of the wealthy as the nation's ruling class.
The Democratic-Republicans were led by individuals like Thomas Jefferson, James Madison, and James Monroe. Democratic-Republicans favored the idea of state governments having more power than the federal government. They feared the idea of a strong federal government, largely because of their experience under the strong federal government of the British prior to the Revolution. They held a stricter interpretation of the Constitution in which the federal government was limited to the powers expressed in the Constitution.
Democratic-Republicans had greater support amongst farmers and saw more of a future based around agriculture. Democratic-Republicans also believed in free trade that provided greater access to cheaper imported manufactured goods. While Federalists felt that the wealthy should constitute much of the ruling class, Democratic-Republicans felt the common people should have more influence on the nation's government. Democratic-Republicans also felt that the United States should have closer ties to France than to Great Britain.