"I have no time or place for weakness. There is only strength."
Little is known of Vegeta's early life, though he was born with a rather high power level. As a teenager his father often sent him on possibly fatal assignments to test his strength, especially the Battle of Polydora, where he briefly lost sight in his right eye thanks to a solar flare.
Vegeta objected to Freiza's domination, using Nappa to pull a hopefully-fatal prank on the overlord. When that failed, Vegeta accepted the fact of Frieza's control.
More to be revealed as The Saiyans and The Forgotten Saiyans continue!
"I thought I put my underwear in the left drawer... NAPPA!"
Vegeta is a serious individual, not really getting pranks and jokes. When he does pull them, however, they usually end up fatal towards the the victim. Raditz often comments that his friend has no sense of humor.
Vegeta heavily respects his father (besides besting him as a child), and has a small friendship with Nappa and Raditz, his only two companions. He had a relationship with Umbra, even fathering a son, Terrax (who will go on to be a protaganist in The Forgotten Saiyans), before breaking it off, as it was distracting him in combat.