How would you have changed DB

[Hades]

The Saiyan's relationship with Freeza (never clearly explained in canon) - The Saiyan Empire had arisen from the Planet Vegeta and had dominated much of the Northern Galaxy for centuries. However, the old Empire began to fall at the seams, as new powers like the Planet Trade emerged under King Cold. The Planet Trade began as a mercenary force which would exterminate the populations of planets for the highest bidder. Over time, the Planet Trade grew in strength as it commanded whole species under its banner, allowing it to challenge the Saiyan Empire for supremacy in the Northern Galaxy. Eventually, King Vegeta decided they were an intolerable threat and ordered the Empire to go to war with the Planet Trade, which would last decades. As both Empires crumbled, Cold realised that desperate measures had to be taken before there was nothing for either empire to win. He remembered legends of "Living Weapons" from the "lost era" and found an abandoned temple dedicated to Huitzilopicthli, one such Living Weapon. There, scientists working for the Planet Trade worked on a formula based on the Living Weapon technology, which imbued Cold and his sons with unbelievable power, before destroying the temple and all documents regarding this Living Weapon to ensure no-one else could use it. However, King Vegeta's spies took some samples and attempted to make some supersoldiers of their own, with little success (Prince Vegeta and Kakarrot were considered failed subjects, while [DATA EXPUNGED UNDER IMPERIAL DECREE 119078.]*). within days, the war had demonstrably turned in the Planet Trade's favour, with Freeza, Cold and Cooler being utterly merciless in crushing their enemies. In the final days, Planet Vegeta itself was besieged by the Planet Trade, with Freeza (already driven insane by the war and full of contempt for the adversary) deciding to incinerate the planet, destroying the last remnants of the Saiyan Empire, save for Prince Vegeta Raditz and Nappa, whom he kept as a trophies from the defeat of the Saiyans. However, just before Vegeta's destruction, Bardock, who led the last stand at Vegeta, ensured the safety of his son Kakarrot by putting him in the escape pod of a ship in the vain hope that he would continue the war years after the Saiyans were gone.

Vegeta's character development (badly handled in canon) - He's one of the last of a fallen civilisation (like The Doctor) and has come to Earth because Goku is the only other remaining member of his species. What drives him to Goku is the fact that Vegeta was the prince of the Saiyans and has worked all his life to be the Saiyan Messiah (Freeza feared above all else the Saiyans gaining the same powers that he did), only to have some peasant take his birthright out of some contrived series of events, while another stranger had denied him his rightful vengeance against Freeza. He then meets a human woman named Bulma, and has a brief tryst with her. As a result, he has a child. However, this child isn't recognised by Vegeta for several reasons. Firstly, he is a bastard child, and cannot claim to be of Saiyan heritage. Secondly, he is a half-breed, which means that Vegeta has corrupted the Saiyan royal bloodline, yet it is the only way to pass the torch of the Saiyan legacy (Racism & Classism Yay!). Finally, after consulting Baba about his child, Vegeta learns that this child will grow up to be the Messiah. How could a bastard child become something that his pure father wasn't, especially since his mother would raise him among the world of men, a society that Vegeta held in contempt as "childlike and immature"?

Majin Buu (rather underwhelming origin story for such a monster in canon) - Aeons ago, there was a war between the Kaioshin and the Demon world (Like the Time War of DB in terms of scope and scale). However, most records of this war were destroyed, but there is mention of "Living Weapons", sentient beings created with unimaginable power. One of them was Majin Buu, a weapon created by Bibbidi in service of the Demon armies. Unlike the other Living Weapons, it could devour enemies and acquire their attributes, like a sentient parasite. Over time, Buu would gain its attributes through this method, which led to it becoming the reason for the end of the War. However, Bibbidi shown his true colours as he used Buu against both Kaioshin and Demon, becoming more powerful until it absorbed the Dai Kaioshin, which somehow mollified this living weapon with a childlike mentality. In the final day of the war, the last Kaioshin slain Bibbidi before he could use Buu to complete his conquest, leading Buu to be lost to time, or so he thought...

*Yeah, I set up the story of Broly