Rito, Goron, Gerudo, Zora. I only started the dungeons after 150 of 152 shrines.
I went Zora, Rito, Gerudo, Goron in BotW (I didn't beat Thunderblight until after I got Daruk's Protection though). I think the Rito quest being the easiest in both games is kind of disappointing, but at least...