As much as I HATE that Todd relies on Batman way too much, he has the most interesting set of characters. So this list will be full of Guano. I won't go for a specific version of characters, except when I really want ONE specific version for example: Batgirl (Arkham Knight) that means that I want an Arkham Knight Batgirl.
But if it said: Hugo Strange with nothing inside parentheses, then any version of Hugo Strange that is not from BTAS is a valid option. But even without parentheses, I might explain which versions I'm leaning towards, but I wouldn't necessarily DEMAND those versions.