I usually play standard deity.
And I manually pick the AI which I feel the most challenging.
Usually, I almost always include Poland,Korea,Greece,
Sometimes Atilla,Shaka,Caesar,Bismarck, Hiawatha, or Siam and I always leave 1 or 2 random civ for different flavor. (but I hate it when they randomly picked overly passive/bad AI)
I cant really remember which civ that always does very bad, maybe Indonesia,Venice,Portugal,Babylon,Brazil,France,Assyria, Netherlands. If possible, I would like that these civs never been chosen for the random opponent AI.
Gandhi also always not doing very well in my game, dunno why. He always stuck with only 3 or 4 city, and almost never war. I read a lot about Gandhi warmongering and nuke in forum or reddit, but I never actually saw it. Note that I usually finish my game before turn 350.
IMO, AI which consistently become a runaway in my game are Greece,Atilla,Bismarck. Sometimes Rome and Shaka.