I’ve never really found turn-based games to be all that fun. A few have had a good enough story or some other mechanic to make them interesting but it’s just not really my thing, for some reason. (It’s not just a video game thing. A bunch of my friends play poker or complex board games and I’d usually rather watch than play.)
So, something like the Final Fantasy series or Pokémon games would be my answer. Everyone loves Final Fantasy and Pokémon. I’m clearly the weird one. And I probably would love them if they were more action-oriented.
I think my all time favorite is the N64. Some aspects haven’t aged all that well — the controller is obviously weird by modern standards — but it was such a huge jump from 2D gaming. It was new and exciting in ways that are almost impossible now.
And I still like how weird it was. There was tons of experimentation by developers while figuring out how this new era would work on top of the usual fun, Nintendo quirkiness in the first party games. The PS2 and Xbox ended up setting the standard for modern gaming controls, optical discs, and all the rest but the N64 lived in a weird, fun transition space between retro and modern.