During the Colonial Era, economically, the Thirteen Colonies were largely understood as an extension of Britain (even if in practice, the colonies were granted much more autonomy than one would expect from Mercantilist policies). Still, the colonies were largely agrarian and much of its commerce was focused on the export of colonial goods back to British markets. Coming out of the Revolution, then, the United States would not have been on anywhere near even economic footing with major European nations like Great Britain, particularly in spheres like manufacturing and banking.
Hamilton's vision of the United States entailed an advanced and (by the standards of the time) modernized economy, stable and self sufficient, and at the same time, he was a champion of Federal power (as opposed to the small government vision championed by Madison and Jefferson). He wanted the Federal Government to take steps to ensure economic investment and economic stability. Setting tariffs and instituting a National Bank were both ways of achieving this vision.
Tariffs actually achieve two ends simultaneously. In a more short term perspective, they are a form of taxation, which means they are a way of financing the Federal Government, and the Federal government would have needed money to be able to support the kind of policies Hamilton envisioned. More importantly, though, Tariffs are a way of safeguarding domestic industry by creating barriers of entry to competing goods. In this way, the US government could act to ensure that then a still fledgling US manufacturing sphere could continue to grow and prosper without being overwhelmed by its competitors.
Similarly, the National Bank, was an institution which likewise served to ensure economic growth and stability, especially when compared to its alternative in State Banks. Banks are primarily investment tools, and a functioning Banking System has historically been a powerful engine for economic growth, and a necessity for achieving a strong and modernized economy. This is something Hamilton would have understood.
Alexander Hamilton supported placing taxes on imported goods and establishing a national bank for a few reasons. By placing taxes on imported goods, the United States government would be able to generate income that could be used to pay our debts and run our country. It also would offer some protection to American industries from competition from European countries. Since our industries were newer than Europe’s industries, the Europeans could make products cheaper than we could make them. Thus, people would buy from other countries instead of from our factories. These taxes would not only generate income for the government, but they would protect our factories from foreign competition.
Alexander Hamilton wanted a national banking system. He knew the government needed a place to put its money. The same was true for businesses and individuals. Without a banking system, our financial system would be less sound. This could negatively impact the economy and our economic growth.
Alexander Hamilton wanted taxes on imports and a national banking system to protect our economy and help our businesses and economy grow.
Alexander Hamilton favored these things because he believed that the US should develop an economy that was mixed, one that had both farms and manufacturing. He believed that high tariffs on foreign goods would help to bring this about because foreign goods would be kept out and domestic industry could get going. He believed in a national bank because it would keep the currency stable and create a stable business environment in which business could thrive. By creating a good business environment and keeping foreign competition away, Hamilton believed that the government could help a mixed economy to develop. This, he felt, would make America strong.