1. Vegeta is gay, but not for Goku.
Nothing changes at Saiyans/Freeza sagas. With no Trunks, Bulma is the one who comes from the future. Androids/
Cell sagas happen without Trunks with no major changes. At Cell Games, Gohan has an easier time defeating Cell,
since he's not wounded to save Vegeta.
At Buu Saga, without Gotenks, either Goku does the reasonable thing and defeats Buu with SSJ3 or Ultimate Gohan
defeats Super Buu later or, if Gohan is absorbed, Vegetto shows up. Super happens with no changes.
2. Vegeta is gay for Goku.
After defeating Goku with Oozaru form, he spares his life and takes him to outer space with him. After they're healed
on Planet Freeza (Goku's PL post zenkai= 10k), Vegeta proposes to Goku to go to Namek together, find dragonballs,
defeat Freeza and then rule the universe as a royal gay couple. Goku does not really get the part about gay couple, but
he's like 'There are guys stronger than you, Vegeta? Yay', so he accepts.
On Namek, Vegeta asks Goku to step aside and defeats Cui and Dodoria himself. After losing to Zarbon, Goku steps in
and defeats him with a 4x kaioken or something. After defeating Zarbon, he goes to find Gohan, Krillin and Bulma and
convinces Dende to heal Vegeta. Guru unlocks Goku's and Vegeta's potential. For simplicity sake, let's say Goku is his
post 100x gravity training self and Vegeta is his post Recoome zenkai self.
Ginyu Forces show up. Hard to say how exactly the fight goes with Guldo's time stop and Ginyu's body swap, but, I think,
in the end, Z fighters win. No way both Goku and Vegeta decide to just sit there and let Freeza do all those transformations,
so Freeza is also easily disposed of.
Androids/Cell sagas happen with Bulma coming from the future instead of Trunks. When the ROSAT comes up, Vegeta
decides to go to the room with Goku. Dunno whether he manages to seduce him in there, but them training together
greatly benefits both of them. No way Goku lets Cell absorb Eighteen, so Cell is killed while in second form.
7 years later, Vegeta does not let Babidi control him, so no Buu. Super happens with no changes.