This is an extraordinarily good question! And as such, it's very hard to answer.
Considering the condition you've set and the Rawlsian principles associated with it, I'm bound to shoot for an anime world with at least some egalitarian aspects. That is, unless I pick a show that eschews implications of the political or the societal on the whole, i.e. uses some intimate, personal setting.
I'd be a fool to pick something like Shinsekai Yori with its subjugated and literally dehumanized masses enslaved by a decadently ignorant elite. There might be some charm to choosing an anime world like YuYuYu's or Zegapain's, in which most everybody is at least equally bad off considering the characters' relative position to the world they inhabit. I'd even consider team-based sports anime such as Ganbare! Kickers; no matter your skills and your position, you're part of something and receive the appropriate recognition. That's nice.
So after some consideration, I think I'd pick one of my recent favorites, Flying Witch. Not too wax too philosophical, but there's a deeply relaxing undercurrent of ataraxia permeating the anime world. Things are alright in Flying Witch. People are comfortable with their place in life, even with the occasional frustrations. Ambitions are achievable. There's fun and happiness and curiosities and delicious radishes and apples. I think I'd enjoy having been born in this anime world, even as an uncredited Boy C and with no special abilities or roles.