I really like tabletop RPs, or just RPs with dice mechanics in general, where it really feels like a game and has some more unpredictability. Character driven rps, rps with a lot of character development, and equal amounts action + chill are also what I think of per the thread question. 

As for specific genre, I love the whole monster catching genre so much, but I love anything with fantasy really. Then there's some fandoms I'm partial to, like Final Fantasy, Persona, and some others.