Aradia was adopted and raised by a very progressive, modern yet hippie-ish woman-led household. It was a somewhat rural area, so they all stood out. She did pretty well in school, and always had big dreams.
Tavros grew up with his grandparents living with them, and was very well cared for. Got the occasional trip to Disneyland because once upon a time that was an affordable option for their tax bracket. went all out for Halloween each year.
Sollux was raised by a gay couple in the city. He grew up playing piano and violin, speaking four languages, and inventing a new equation here and there. He did not like any of that boring stuff though, what he REALLY wanted to do was build contraptions in Minecraft, grief people's builds, and retire at age 16 so that he never has to work. Unfortunately, he fucked up that last one and is only on the path to retire at age 35. Sad!
Karkat was raised by his grandparents. They partied a lot, but there weren't usually other kids at the parties so he often hated it. Lived in the oppressive suburban sprawl. Was surprisingly popular in school, and tried his damnedest at everything he did, but often he's clouded with feelings of being mediocre, and that definitely did not go away when a sports scholarship he wanted went to vriska. Discovered romance when he watched Love, Actually on cable TV, and, well, you know the rest.
Nepeta was ALSO raised by her grandparents, in a trailer park. Grew up hunting, and fishing, and exploring. Discovered romance when she looked up "cat drawings" on the family desktop and stumbled upon DeviantArt, where there were hundreds of Warrior cat ships. This opened a Whole New era of Nepeta. Also her pet cat got hit by a three wheeler when she was, like, 13.
Kanaya had a quiet but strong single mother that taught her as much as she could. Her childhood was a little bit strict in terms of behavior, but at the same time, she was given more intellectual autonomy than most her age. "She was a pleasure to have in class!", wrote Ms. Woiblet.
Terezi was latchkey as fuck, just running around, experiencing the world without a leash. Got into hella trouble. Also she was a cookie monster pajama girl, her best friends were freaky goths and out gay guys, and she always had a big ass bag of hot cheetos on her. The lawyer thing was a surprise to some people when it happened.
Vriska was also a latchkey and troublesome child. She pushed other kids off of playgrounds, and eventually started pushing them into lockers when they got older. She has pushed every counselor to the brink. She was actually good at school, and eventually someone convinced her to do rugby, thinking it would give her an outlet.
Equius was a sporty kid with rich parents. He was lonely and easily ostracized, but still got to hang out with kids his age on DeviantArt (that's how he met Nepeta). As a teenager he was only more awkward, not at all helped by his increased height. Most girls didn't like him. Got voted "most likely to break their phone" in his high school's yearbook.
Gamzee started a philosophy club at his high school. It was mostly just dinkin around.
Eridan grew up rich and well-connected, although her parents didn't know what to do, emotionally. She was bullied for liking littlest pet shops, and he NEVER got over it. They were a troubled kid, and ages 12-18 they got a lot of counseling. The only thing that gave her a proper outlet, though, was theatre camp and drama club. More problematically, he also found an outlet in causing drama. They almost went down the alt-right pipline but by the beautiful brace of God they found out about being gay instead.