Astronaut
The first civilian in space was Valentina Tereshkova aboard Vostok 6 (she also became the first woman in space on that mission).
Tereshkova was only honorarily inducted into the USSR's Air Force, which did not accept female pilots at that time. A month later, Joseph Albert Walker became the first American civilian in space when his X-15 Flight 90 crossed the line, qualifying him by the international definition of spaceflight. Walker had joined the US Army Air Force but was not a member during his flight. 
The first people in space who had never been a member of any country's armed forces were both Konstantin Feoktistov and Boris Yegorov aboard Voskhod 1.
Mercury 13
Although both Cobb and Cochran made separate appeals for years afterward to restart a women's astronaut testing project, the U.S. civil space agency did not select any female astronaut candidates until Astronaut Group 8 in 1978, which selected astronauts for the operational Space Shuttle program. Astronaut Sally Ride became the first American woman in space in 1983 on STS-7, and Eileen Collins was the first woman to pilot the Space Shuttle during STS-63 in 1995. Collins also became the first woman to command a Space Shuttle mission during STS-93 in 1999. In 2005, she commanded NASA's return to flight mission, STS-114. At Collins' invitation, seven of the surviving Lovelace finalists attended her first launch, ten of the FLATs attended her first command mission, and she has flown mementos for almost all of them.