The first game I ever played of the genre was probably Wandering Willows. It’s quite old, release was in 2009. It was very different from all the other games I played up until then (which was mostly Final Fantasy, Zelda, Mortal Combat and the like xD).
You are stranded on an island and have to fulfill quests and help the villagers. As a companion you can catch various pets and level them. There is also farming and character customization.
Probably Animal Crossing: Let’s Go to the City which my parents bought me around 2011 I think? I loved the idea of decorating my house and being a nice neighbour and planting nice flowers everywhere. My favourite memory about the game was a musician who would come to the town on Saturday at 20:00(?). My cousins and I often chilled together with the game’s music running in the background ^^