Some important post-film divergences for my (default) portrayal:
While it's true his family / home life is 'fixed,' as his mother isn't an alcoholic anymore and the environment isn't as toxic... his family are total strangers to him. He's in a life he doesn't know, he's replaced another him who may or may not be a completely different person, and the more he stays in the fixed timeline, the more he realizes that pretty much nothing around him is familiar anymore, they're all different in little ways.
As a result of his time travel, many death and near-death experiences, and messing around with the timeline, he suffers from some undiagnosed aspects of PTSD and depersonalization-derealization disorder. Also, he has some issues with self-hate / self-doubt / inferiority and has a massive chip on his shoulder, like in canon, but this lessens with time.
He spends as much time as he possibly can with Doc, as Doc is the only constant and the only one who both understands and who hasn't changed that much. Marty is also drawn to Doc as they've been best friends for a long, long time, so he relies on him a lot.
While I think Doc basically raised Marty to get him away from his awful family in the original timeline, which Marty remembers, Doc may or may not remember as he wouldn't have done that as much to amended!Marty in the amended timeline. If he doesn't remember, this makes Marty very upset, understandably so: he feels like he's lost the strongest parental figure he's ever had all over again.
He goes to community college in Hill Valley and lives with Doc, having a major in music or composition and a couple minors in science / engineering / mechanics thanks to his work with Doc.
They never stop time (and space, they add modifications so that they can go places on Earth and beyond) traveling (I'm not really BTTF 2 or 3 compliant by default)
However, they have to workshop it and a lot of the time it doesn't work when they test it, especially early on, so sometimes Marty just shows up at any time and any place
They do have a time and space stable method of communication (I've dubbed it the time-phone but it's a dumb name) and another time machine (either the train or another deLorean) so that Doc can always find him no matter what
He does end up releasing records / becoming a pretty big musician and touring, the band name changing from The Pinheads (their first audition tape) to McFly and the Flyaways
In verses where he marries Jennifer, their kids are named Emmett George and Elizabeth Lorraine, not Marty Jr. and Marlene, because canon what the hell