I'm thinking about the games I played in my childhood that influenced what I like to play now, so it might be only halfway relevant to the question.
First monster collector: Pokemon Blue. Digimon World 1 was also one of my favourites, because of how real it felt, like a real monster. The one other monster game I really got into as a child was Dragon Warrior Monsters 2, I think I played Cobi's journey. It helped that a lot of my friends were playing it.
First builder: Simcity 3000. Started my lifelong love for city builders, even though I'm not great at them per se.
Theme Hospital and Dungeon Keeper 2 were my introduction to management sims and also my favourites for a long time.
As a kid I absolutely loved this RTS called Warbreeds because of the ability to graft any weapon onto any unit. Nowadays though I just find such mechanics fiddly, but as a kid it felt so sci-fi. In terms of time spent playing, though, the standout RTS was probably Starcraft.
I also played on a lot of MUDs as a kid. Wheel of Time (but had never read the books), Discworld (but had also never read the books), Aardwolf and I think one or two others. I was amazed at how it felt like I could do so much (even though most of the "free" actions were just emotes.
My first graphical MMO was I think Maplestory, which was a huge part of my social life as a kid. I think I miss the feeling of being part of a big community than the MMO experience itself, honestly. Nowadays when I try getting into MMOs it feels like that feeling of being a part of a giant community of people is gone.