The program began with the various designs and estimates that were given to Nixon and his Budget Office, and in 1972, they gave a go ahead for a specific development plan. After the system was developed, the first prototype, Enterprise was used in drop tests that validated the last portion of the return to Earth phase. As well, Enterprise was used for pad fit tests before an operational shuttle was available.
Columbia flew the first Shuttle orbital flight April 12-14 1981.
Challenger was destroyed on Jan 28, 1986.
The Gemini program ended on Nov 15, 1966, with the landing of the last Gemini mission, Gemini 12, so the Gemini program was long before the Shuttle, and had nothing to do with the Shuttle program. Apollo came after Gemini and before the Shuttle.