You could pursue the theme of American empire on the seas, and the growing power of the US Navy at a time when World War I was approaching. You could also concentrate on American diplomacy, as Teddy Roosevelt became sort of the first President to be a world diplomat - in terms of negotiations between other countries in the interests of peace. Wilson and his Fourteen Points, and pursuing the Treaty of Versailles should give you plenty of material.
The Spanish-American War 1898 was fought between the U.S. and Spain while McKinley was president. Often referred to as 'A spendid little war', it was clearly motivated by the U.S. desire to expand it's influence (American Imperialism) Officially the U.S. stated that Spanish policy in Cuba was close to violating the Monroe Doctrine (no further colonization or influence in the western hemisphere), however the mysterious explosion of the U.S.S. Maine which Spain was held responsible for gave the U.S. the jusification it needed to go to war. The U.S. won the war and as a result gained a military base in Cuba, possession of the Phillipines, Samoa, Guam, and Puerto Rico.
President Theodore Roosevelt further expanded U.S. imperialism (expansionism) The Roosevelt Corollary added 'international police power' to the Monroe Doctrine, which meant that the U.S. had the authority to protect it's interests in the western hemisphere, in other words the U.S. was the self proclaimed power authority in the west. Obviously, this was the cause of great resentment by the Latin American nations.
These two examples should give you a start, however you should further investigate Teddy Roosevelt, (Panama Canal) Many historians do credit Teddy Roosevelt and his 'big stick policy' for better or worse, as the man who transformed the U.S. into a world power. The administrations of Taft and Wilson also contributed to the interpretation of the Monroe Doctrine and U.S. influence on a global scale.