Canon?

[Kazuya]

Chubbs has its own history, and doesn't stick too much with the show, although, there are some elements (Such as the Oozaru and namekian regeneration, or Red Ribbon Army, etc.) that we keep around, but they are tailored to fit our world. The only thing that has to stick basically, is family relations, although, if, for example, Bulma, wanted to engage in a relationship, with say, Goku, that's ok, but, Trunks and Bra would still be her children, and Vegeta would still be their father.

So, in a nutshell, we are our own universe. ^_^

EDIT: And also, you can tailor your character to how you want, as long as appearances stay pretty much consistant with the manga/show version.

[Kazuya]

No problem. Welcome to Chubbs. =)