The Captain has gone by many names, by many historians. However, most final historical records indicate that the key figure in the defeat of the Ur-Quan Hierarchy was a human named Zelnick. [In particular, there was no default name in the first release of the game; the first act in a new game was to name the commander and the flagship. The 3DO version named the Captain and the flagship Zelnick and the Vindicator, respectively.]
Zelnick was born on the the colony world of Unzervalt and showed an unusual aptitude for reverse-engineering Precursor technology. He captained and piloted the SIS from Unzervalt back to Earth, and is generally agreed to have played a pivotal role in the events of the quadrant from 2154-2159.
Full details on The Captain are sketchy; only one known image is available of Zelnick during his time as a Captain. [This being the Escape Pod sequence.] From it, and from knowledge of the history of Unzervalt itself, we can conclude that Zelnick was human, male, predominantly Caucasian, and under 20 Earth years old at the beginning of his mission.
He is probably one of the most legendary humans ever to travel the stars.