In classic Dragon Ball I think there are “only” 5 main story lines, with thematic overarching plot lines and character arcs, as opposed to the lists with many different sagas and arcs. What do you think?
The Legend of the Dragon Balls:
From Bulma bumping in an orphaned boy on her quest for the magic dragon balls to said orphaned boy meeting his deceased grandfather one last time - before finally using the dragon balls for something good and selfless, after having many adventures during which our heroes face evildoers who want to use the dragon balls for evil and selfish purposes.
Demon King Piccolo:
From the 22TB to the 23 TB: Goku and friends face a demon from Muten Roshi’s ancient past. Goku overcomes this threat by defeating the demon (twice), shows him mercy, surpassing not only his former master, but also the demon, God and becoming world champion. This arc has a nice thematic subplot too, where Goku and friends face and befriend the students of Roshi’s rival who also has a history with said demon.
The Legend of the Super Saiyan:
Goku discovers his alien heritage, and faces his surviving fellow Saiyans - who turn out to be evildoers who where whiped out by an even more evil tyrannical overlord. The arc comes full circle when good hearted Saiyan Goku becomes the first Super Saiyan of Legends and defeats the galactical overlord.
Hope for the Future:
Trunks goes back in time to save the world from the evil androids. The future is a main element of the story. It’s about changing the future, but also about passing the torch to the future generation. It’s Goku that sets the story in motion (his actions lead to the androids, to the coming of Frieza and Cold. His death leads to a future without hope). The story comes full circle when Goku dies regardless, but his actions inspired the next generation (Gohan in the main timeline, Trunks in the future one) to overcome the threats.
Majin Buu:
The story starts with the 25TB and ends with Goku flying off with Uub. Main themes are passing the torch (Gohan, Goten, Trunks and Uub at the end), but also antiheroes finally having their heroic moment against an almost invincible enemy (Vegeta, Satan).
I could also do a similar break down for DBS, but I must admit I know that one less well