Well, it could vary a lot. In some fanfics, Bardock might be reborn with new powers or a different destiny. Maybe he gets to change the future of the Saiyan race. But it really depends on the author's creativity.
Obviously, Bardock is one of the main characters since it's about his rebirth. Goku might also be involved as Bardock is his father. Vegeta could potentially show up too, as he is an important Saiyan in the Dragon Ball Z universe.
One alternative is to focus on character backstories. You could write about the early days of Piccolo, how he came to be the way he is. Another option is to do crossovers with other non - sexual universes. Maybe a story where the Dragon Ball Z characters meet characters from a magical anime world and they have to work together to solve a problem. Also, you can write about the relationships between the characters in a platonic way, like the deepening of the friendship between Gohan and Krillin.
The full story of Dragon Ball Z is about Goku and his friends protecting the Earth from various powerful villains. It starts with Raditz arriving on Earth, revealing Goku's Saiyan heritage. Then there are battles against the Saiyans like Vegeta and Nappa. Later, the threat of Frieza emerges on Namek. Goku transforms into a Super Saiyan for the first time to defeat him. There are also the Androids and Cell arcs which bring new challenges.
Dragon Ball Z is both anime and manga. The anime was adapted from the manga and they share the same story and characters, but presented in different mediums.
A Kryptonian in the Dragon Ball Z universe could potentially be a very powerful addition. Their natural abilities like super strength, flight, and heat vision could make them a force to be reckoned with. However, they would also face challenges as the Dragon Ball Z world has its own power scale with ki-based powers. They might have to adapt to the different fighting styles and power sources. Maybe they could learn to use ki in addition to their Kryptonian powers, or they could find a way to combine the two in unique ways.