I've watched too much anime already, I loook for games that do something differently. You might like Dragon Quest 11 more than the other ones since they put more attention on the story telling, from what ive seen. But maybe also it isn't what you look for in a game at this time. Dragon Quest has what it does to offer, and it's pretty great, but a deeply involving story that's shoved in your face a lot isn't that. At least not up to DQ10. Final Fantasy would probably more up your alley, although there isn't much choice, unlike persona if you play that then you can build the relationships you want. There's lots of different games around that offer all their own things.
I will say though that no game has really pushed what's possible with relationships in rpgs. I guess Rune factory has some stuff, but the story isn't deep and involving, so it's hard to think of something that has both. Anyway, the more you know what you're looking for, the easier it'll be to know what you want to be in for in the games you want to play. At the same time when you get what youre looking for you can also spread into other areas. And like, I wouldn't use dragon quest for my source of deep involving stories, that'd be anime or movies. Or I could play Final Fantasy to get a mix of both.
I might be interested in an mmo at some point, dragon quest or final fantasy. I do like that kind of gameplay too, and usually it's easier to choose how much lore you want to see or not. Anyway that's just something i could look for in a game. (for one side of fun, anyway)