For the United States, the major consequence of this war was that the US became an imperial power. Up until that time, the US had taken very little in the way of overseas territories. But with this war, it came to have possessions in the Caribbean (Puerto Rico) and in Asia (Guam and the Philippines).
By winning this war, the US came to be much more willing to throw its weight around in world affairs. The US started to intervene in Latin America under the Roosevelt Corollary to the Monroe Doctrine. It started to insist on being taken seriously as a power in Asia, with the Open Door policy and with Roosevelt’s mediation of the Russo-Japanese War.
All in all, the war made America much more aggressive in foreign affairs and made it into an imperial power.