Gohan is the son of Goku and Chi Chi. He was not a fighter at the beginning of DBZ because he had to study, but when Radditz arrived he was kidnapped and he showed how strong he really was. He saw his father about to be killed by Radditz which made him break through the space pod because of his giant power level increase. After the battle with Radditz in which Goku sacrafices his life, Gohan is trained by Piccolo and over time Piccolo becomes his mentor. He goes to Namek to fight and his power level increases, but it isn't until the Cell saga that he starts to shine. When he battles Cell he talks to Android 16 and when Cell kills him he becomes inraged and goes SSJ2. After that Gohan becomes the Great Saiyaman and defends the city. He goes to Orange Star High School and has a girlfriend named Videl who he has a daughter named Pan with.
Goku was found by his adopted grandfather,Gohan. Goku was an
evil boy until he fell and hit his head. After that he was a kind,nice(dim)boy. The whole dragonball series starts when he meets Bulma a young girl on vacation searching for 7 mystical speres called dragonballs. These dragonballs were used to summon Shen Long the dragon. Whoever summoned the dragon received a wish. Goku rides around on his little yellow cloud Candy Cloud(or Nimbus). Goku later finds out in Dragonball Z that he is of a race called the sayajins. Goku is the main character of the dragonball series'. He has two kids with Chi-Chi,Gohan(named after his grandfather)and Goten.
Trunks is the son of Vegita and Bulma. He comes from the future to warn the Z fighters of two androids who will kill all of the figters except Gohan(who later dies). He gives Goku a medicine from the future that will save him from the heart virus that kills Goku in the future. When he first comes, he turns S.S. and wipes out Frieza quickly and blasts King Kold. Trunks comes back when the androids arrive. He tells everyone that the androids from his future are different. The androids from his future are later introduced. He then finds out that a creature from a third reality kills him and takes his time machine to come to this reality, Cell. Trunks trains in the hyperbolic time chamber. When he comes out he is an "ascended sayajin"(Ultra SSJ). He is in the Cell games and watches the fights. When Cell comes back is killed by a kai shot. He is wished back though. He appears in some of the movies. When he arrives in his own time he destroys the androids and than faces off against imperfect Cell. He fights and beats Cell an than starts with his life without the androids. He appears in the last episode of DBZ.
Vegeta is a cold hearted warrior with only one thought in his mind...to become the strongest warrior in the universe.
He starts out as a bad guy at the beginning of the series and ends up a good guy. He can never quite grasp the concept
that Goku, a common sayajin could be more powerful then himself, a prince from a royal bloodline. He has two kids with Bulma, Trunks and Bra.