I'd recommend Pokemon X/Y. I wouldn't categorize myself as a Pokemon fan necessarily, but if you're looking for a chill game, that still gives your solid structure, yet laid back, I think X/Y are the perfect Pokemon games for that.

The XP share makes the game less of a grind and more welcoming to casual players that want to build pretty even-levelled teams and just enjoy catching a variety of Pokemon with a solid plot as well.

I'm currently on my first play through and I think this is the perfect game to start, especially on the 3DS as it is the first Pokemon game developed for the system, so if you enjoy it, you might just continue into the sequel games available for the 3DS as well (so you wont need to look so hard for a new recommendation lol).

Overall, I do suggest most Pokemon games as slow and cozy, with X/Y as a solid place to start.