Roamy here. When astronauts train or otherwise get their flying hours, they fly T-38 Talons, the first supersonic jet trainer.
First built in 1961, they replaced the T-33 Shooting Star trainers (which both Roamy’s dad and XBradTC’s dad flew). The F-5 Freedom Fighter and F-20 Tigershark were derived from the T-38 airframe design. Over 1,100 were built, and there are several variations, including adding a gunsight and gunpod for weapons training aircraft.
T-38’s were flown by the Air Force Thunderbirds air demonstration squad from 1974 to 1982, though that ended with the infamous “Diamond Crash” near Creech AFB, Nevada. The team was practicing a four-plane line abreast loop, when Major Norm Lowry’s pitch control actuator malfunctioned. He, Capt. Willie Mays, Capt. Joseph “Pete” Peterson, and Capt. Mark E. Melancon were supposed to level off at 100 ft after the loop and instead nearly simultaneously crashed into the desert floor. When the Thunderbirds resumed flight demos in 1983, it was with F-16’s.
It’s on Wikipedia with no citation, so take this with a grain of salt, but it has been said that 50,000 military pilots have trained on the T-38. Even though the last one was built in 1972, a couple hundred T-38A’s are being rebuilt to the T-38C standard, with an all new glass cockpit very similar to those in modern jet fighters.