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.
Jeannette Piccard
Piccard was the first licensed female balloon pilot in the U.S., and the first woman to fly to the stratosphere. Accompanied by her husband, Jean—a member of the Piccard family of balloonists and the twin brother of Auguste Piccard—she reached a height of during a record-breaking flight over Lake Erie on October 23, 1934, retaining control of the balloon for the entire flight. After her husband's death in 1963, she worked as a consultant to the director of NASA's Johnson Space Center for several years, talking to the public about NASA's work, and was posthumously inducted into the International Space Hall of Fame in 1998.