Goku made his first appearance in the first issue of the manga, "Son Goku" in the Japanese magazine "Weekly Shonen Jump." He is also in the first episode of the anime. Vegeta doesn't make an appearance until chapter 204 of the manga, and the sixth episode of the anime series.
Goku once thought he was a human, even though he had a monkey tail. Later he learns that he is from the alien race of the Saiyans. Vegeta was born a prince of the Saiyans.
Vegeta has superhuman strength, super speed and reflexes, and the ability to fly. He is also able to do transformations into more powerful forms. Goku has similar powers, plus he can teleport to any planet and perform energy blasts.
Vegeta wants to gain all of the Dragonballs in order to gain control of the universe and live forever. Goku wants the Dragonballs to save his friends and family and to prove his own worth.
Goku is the first warrior in 1000 years to achieve the Super Saiyan level. Though Vegeta longs to be the strongest, it is Goku who is the most powerful.