With my parents, it's one story each. My mother was exposed to it as a child because my maternal grandparents were in it from young adulthood, I think (this would be shortly after WW1). My mother wasn't heavily involved as a youngster because my grandparents weren't pushy about it towards their kids - indeed, they appeared to become heavily disillusioned with it as they aged.
When I was very young, I recall major problems at home. I later understood that my father strayed outside the marriage with several women - and he drank a lot.
So, both parents were disillusioned with life generally, and sought a way to improve things. The first port of call wasn't the JWs though. My father's upbringing left him with negative feelings to the Church of England, and he wasn't too enamoured with more traditional churches. He even gave the Mormons a hearing, but I suspect the alcohol ban may have been a greater deterrent than anything doctrinal.
The JW's came onto the scene when my father asked an old drinking friend how he had turned his life around and repaired his marriage. Oh dear! It transpired that he had become a JW - and that is where the rot set in. I imagine that guilt did the rest, wanting to make amends to his parents-in-law for messing up their daughter.
It probably didn't help matters that my father was adopted in his first year, and only discovered this by accident (he found his adoption papers while looking through the family records as a kid). His step-parents never told him, and it only slipped out many years later that he was aware. So, I suppose he may have viewed the JWs as a quasi-family setup and it fulfilled something for him that had been missing.