What Is America's Place On The World Stage?

I am currently working through research material and notes for my upcoming lecture on American Exceptionalism vs the World Context. As I do this a looming question relentlessly agitates me. What is America's place on the world stage? Is America supposed to be a police force of all nations? Does it have a place at all outside of its own borders? Perhaps America's place is to be something of an influence diplomatically.

In the beginning of American policy non-interventionism reigned supreme. This was tested during the French Revolution when George Washington refused to get the U.S. involved even after France assisted the Colonials in winning the Revolution. Later the Monroe Doctrine would arise reinforcing these old tenets. In the meantime, the United States did often venture out into the world in trade which led to conflicts like the Barbary Wars. This was due to U.S. merchant ships coming under attack and not due to American intervention abroad. However foreign intervention did eventually take place.

The concept of Manifest Destiny helped to expand the United States beyond its Atlantic Coastal colonies through the Ohio River Valley and eventually to the West Coast. Mass land acquisitions lead to the expansion of U.S. territory: the Louisiana Purchase, annexation of Texas, and the Mexican-American War brought not only new territories but also new conflicts with other nations. Though this does not seem like a typical international affair because of its isolation to North America, it is undeniable that the U.S. in the early to mid 19th century began active expansion across national set boundaries by invading other countries, namely Mexico.  The Civil War brought with it strong internal problems to say the least for the United States but after its conclusion the U.S. ventured out into the world. With that being said I would like you to read over Theodore Roosevelt's "Navel War College Address" in June of 1897." You can also see it altered but artistically presented below by Tom Berenger in the movie "Rough Riders."

It is obvious that the United States made the decision after the Civil War and perhaps even before that the time for an emergence on the 'World Stage' was imminent. So I ask, why was that emergence necessary and why was it deemed necessary at the time? Finally, what roll does the U.S. have in the world today if it should have any at all?