Not sure how would I really writte DBS from the point of DBZ's end. Tho, I know how I would (re)writte from Buu arc.
1. I would left new generation (Gohan and Gotenks) take care of Buu, just like Goku intendent.
2. Left Goku stay dead and train in the Other world, as well as Vegeta (who died just like in the manga, and I would make him go to the heaven, he atone for his sins fighting with Galactic Army, Androids and Majin Buu).
So DBS now.
1. Beerus arrival, interested in SSG, goes to fight with SSJ3 Goku, wins easily, go to the Earth to find Prince Vegeta (Vegeta is dead, got his day on the earth, for Bulma's birthday). Story goes same way (+ Vegeta goes SSJ3, which he achived in Other World), but instead of Goku coming back to the Earth, Gohan would fight against Beerus. Gohan became SSG and same scenario happen as in the original manga.
2. How did Gohan achive SSG? First I would change, way of achiving SSG. It was stated that way of achiving is written in some Namekian book, and with Namekians one more character would know about it - Old Kai. The way is simple to surpass previous three states of Super Saiyan as well as surpassing SSJ3's main flaw - time limit. With that knowledge Old Kai created special Mystical technique for drawing full potential of everyone (not only Saiyans), but that method is not effective like original, and gives lesser increase. So, basicually Gohan was partial SSG against Buu, with further training (in my version he woudln't stop) he would achive full SSG during the time of Beerus arival.
3. Next, is Frieza's arrival, except in my version it wouldn't really be a Frieza. Well, Frieza having such big potential is pretty huge plot hole, because of numeros reasons:
- Frieza not training and being born as that strong is not possible considering he used to eat a dust from his parent (King Cold) as stated in the Namek arc, and it was stated that Frieza is stronger than his father, which mean that he surpassed him in some period, which mean that he did train.
- It was also stated that Frieza lost to Beerus once, badly. If he did lost to him, why didn't he train then to beat him, just like he did train to fight Goku?
- And Sorbet and others coming to Earth, searching for DBs and still Gohan, Piccolo, Tien and others didn't do anything to stop them (they felt their power)? Why?
No, no matther how I like Frieza as a villain, he wouldn't be here.
But,..
3. His son would be present there.
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. He was left on unnamed planet to train and one day sucess his father and grandfather (as Frieza was mutant and stronger than numeros time more powerful than other members of his family, same would be with Kuriza). When he heard his family was defeated by Saiyans, he decided to train to one day destroy them. With him
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trained as well and they have become stronger than original Ginyuu force. And in the arc enemy would still be Sorbet, Tagoma, Shisami and Guarana.
4. On the good side of the universe, Gohan left to Whis in order to train, achiving SSGSS, in Other World Goku and Vegeta went to Old Kai in order to achive SSG and on the Earth youngsters train.
5. Fight begins on Earth, and Krillin, Yamcha, Tien, Chiaotzu and Piccolo got their chances against Galactic army - new Ginyuu force and Sorbet's elite. They win against them, but once Kuriza steps in they are defeated without much effort, Gohan arrives and fight with Kuriza (the scenario similar to what happened in Vegeta/Goku vs Frieza).
Next arc.
1. Would make Champa more serious, he gives vibe of one lame character and personality.
2. Tournament.
3. Hit, Froze and Cabba are present, but Cabba still has his tail. Botamo and Maggetta are kind of lame designed characters so I would likely change them.
4. In Beerus team there is no Monaka, pretty sure it's too late to introduce someone so strong from U6, not to mention it was numeros time stated that Saiyans are strongest race. In Beerus team, there will be Gohan, Buu, Piccolo and not really sure should other two be new generation - Goten and Trunks, or older generation Goku and Vegeta. By the time of the tournament, Goku and Vegeta would achive SSG and Goten and Trunks would achive SSJ3.