Different Paths

Saiyans
members of the former Planet Vegeta. Originally led by an unknown king, who decided to stay on the original Saiyan Planet with few as a hundred followers, while most departed for a new home. Led by Vegeta the first, the Saiyans invaded Planet Plant and successfully eliminated the Tuffles. The Saiyans then named Vegeta the first, king, and named the Planet, Planet Vegeta. Soon after, Frieza came with an army and invaded Planet Vegeta. They killed many Saiyans, until Frieza forced King Vegeta to make the entire remaining Saiyan population loyal to him. Many Years later, after Frieza has destroyed Planet Vegeta and most of the Saiyan race, some has survived. On other planets doing missions, or born their from their parents. Some who may have intermingled.

Goku
A Saiyan raised on Planet Earth by Martial Arts Master Grandpa Gohan, after being sent there as a baby to destroy it, he hit his head and forgot his mission. After many adventures, Goku turned Super Saiyan and defeated Frieza, and the Ginyu Force. He also defeated Cooler, then killed him with Vegeta.

Vegeta
The Prince of all Saiyans. Goku's Rival turned close friend. He defeated Zarbon and Dadoria and helped defeat Cooler.

Trunks
The Half-Saiyan son of Vegeta and Bulma. He came from twenty years in the future to warn Goku of a heart virus. When Goku defeated Frieza, he didn't really kill him. So, a year later, while Goku is making his return home from Yardrat, Frieza and King Cold invade earth. Trunks dispatches both them easily, finally putting an end to Frieza's reign of terror.