The US came relatively late to military aviation, which has been often blamed on the drawn-out patent squabbles between the Wright brothers and, among others, Glenn Curtiss, over the "wing-warping" method of control. These went on from 1909 through to 1917 when - with the US entering the war - the government stepped in to "encourage" the aircraft industry to play nice and establish a patent pool.
This wasn't to say that there was no military aviation in the US prior to 1917, of course, with the Army Signal Corps trying out from 1909 various aircraft including variations on the original Wright Flyer. One of the most successful of these was the Curtiss JN-4, which was nicknamed the "Jenny".
However, between the late start and the difficulties of shipping fragile aircraft over the Atlantic, the majority of types the US Expeditionary Force used in combat operations were British and French types; in particular the US "pursuit" squadrons (as fighters were known by the AEF) would become identified strongly with the French SPAD S.XIII design. On first arrival, though, with the SPAD having been chosen to equip the French Air Service too, there weren't enough to go around and the AEF first received the Nieuport 28, last in the series of successful Nieuport fighters but which had lost out to the SPAD in the trials. The Nieuport 28 thus became the first fighter aircraft operated by the United States. Several American squadrons also equipped the famous Sopwith Camel, and there were plans to licence-build the S.E.5a in the US but only a few had been built by the end of the war. Neither British type ever really became identified with the AEF the way that the SPAD was, though.
As for two-seaters (bombing and reconnaissance), again it was mostly French types, the Breguet 14 and Salmson 2 - though again there were some older British types like the Sopwith 1½ Strutter and the Airco DH.9 in use - especially in the early days as everyone was scrambling to find whatever planes could be spared for the newcomers.
Finally, a small portion of the AEF was sent to the Italian front where they were equipped with Italian aircraft: the Ansaldo SVA fighter and Fiat SIA 7 two-seater.
Edit: Further reading -
https://www.amazon.co.uk/Joshua-Levine-Prayer-Pioneering-Aviation/dp/B00I60LAWI