The National Security Act of 1947 established the United States Air Force as its own branch of the military. At that time, there were already a number of aircraft in use by the military. In fact, the U.S. Army and Navy had used airplanes quite extensively during World War II. Therefore, there is no one true first aircraft of the United States Air Force. However, there were air divisions dating back to 1907 that are considered incarnations of the USAF. The first of those had the first military aircraft in the world.
The first air division in the United States military was the Aeronautical Division, Signal Corps, which was established on August 1, 1907. In 1908, under the eye of Theodore Roosevelt, the division bought the first aircraft in military history. There were two that year, a dirigible from Thomas Scott Baldwin and a Wright Flyer from Orville and Wilbur Wright. Both of these aircraft differ greatly from even their World War II counterparts in price and design. Together, they cost roughly $31,750.
The first military aircraft was certainly the lighter-than-air dirigible. It arrived in July of 1908. On May 26, 1909, it made the first flight ever with a full crew of military men. The Wright Flyer, with its heavier-than-air design, was the first proper airplane in the military. This is one way that it made history. Another is that it was the first airplane with a crash that resulted in a death. On September 17, 1908, the Wright Flyer crashed with Orville and a lieutenant on board. The lieutenant died.
In the end, both the Wright Flyer and the Baldwin dirigible have their own places at firsts in military history. Clearly, the dirigible did not have many practical applications as the history of war in the air began, but it remains the first aircraft and the vector of the first fully military flight. The Wright Flyer set the standard and can easily be said to have been the starting point from which all modern aircraft came.