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 the first release of SC2, 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 later released 3DO version named the captain Zelnick and the flagship the Vindicator.]
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, that of directly after his escape via Escape Pod from the destruction of the Sa-Matra, is available of Zelnick during his time as a captain. From it, and from knowledge of the history of Unzervalt itself, we can conclude that Zelnick was human, male, probably Caucasian, and under 20 Earth years old at the beginning of his mission.
He is one of the most legendary humans ever to travel the stars.