Dragonball Z – Dragonball Z follows the adventures od Goku as an adult and has two children throughout the series Gohan and Goten.

this is the best of the series of DB,DBZ and DBGT

finally there is Dragonball GT – which follows the adventures of Goku as a garndparent but he was put under a curse type thing wherein he was turned back into a kid.

DBGT was not an original manga , but an original anime

DBGT was not liked by many DB,DBZ fans

The second one is Dragon ball Z.In this Goku is an adult witha son Gohan.This is the longest series that features many characters.It has 13 movies.Goku comes across villians like Frieza,Cell,Androids and Majin Buu and some other villians.

The third one is Dragon Ball GT.Goku is an adult in the beginning but pilaf summons the black star dragon from the black star dragon balls and wishes the dragon that goku should become a kid again.Th whole series is based on black star dragonballs.Goku comes across enemies like Baby Vegeta,Super android 17,And the 7 Shadow Dragons.Goku and Vegeta become super saiyan 4 in this series.In the end when goku defeats the 1 star shadow dragon(Omega Shenron)the real eternal dragon comes and asks goku to come with him.Then the dragonballs dissapear also.I still dont know that whether goku dies in the end or something else happens to it.In my opinion Goku goes forever but it doesnt seem like he dies.This series has 1 movie.

There is a fake series called Dragon Ball AF(After Future)
Dont believe it.It is a fake series although there is a lot of information of it over the net.