What were three reasons the US followed a policy of imperialism at the turn of the century?

I will assume here that you mean the turn of the twentieth century, since that period marked the rise of the US as an imperial power. Their defeat of an old colonial power in the Spanish–American war in 1898 put them in a position to become a major player in the game of empire.
American imperialism was an extension of the idea of "manifest destiny," a particularly American notion that the US was the vanguard of democracy and freedom and it was their duty to expand in territorial terms. This was also an idea of American exceptionalism. As the West had been tamed in the late nineteenth century, America looked beyond its continental borders to larger international interests.
Imperialism was also a logical extension of America's role in the world. Imperial expansion, from the Philippines in the Pacific to Puerto Rico in the Atlantic, marked an important change in American influence, which up to that point had remained focused on the North and South American continents following the Monroe Doctrine. Imperial expansion allowed the US to open up new markets and it was a spur to economic development.
Finally, there was a racial undertone to American imperialism, which might be seen as manifested in the idea of the "White Man's Burden," a concept first embraced by Theodore Roosevelt. There was the idea that American imperialism should be embraced to secure the future of the "European race." Aspects of US imperialism since the early twentieth century have arguably involved the suppression of democracy in non-Western nations.