`t` comes first or comes last when designing a library

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I would say it depends on how your functions are intended to be used. From my point of view, the general form of a function’s type is a -> b, i.e. it is something that transforms an object of type a to an object of type b: a morphism. So when I see a function with the type a -> b -> c, I see it as a family of morphisms from type b to type c parametrized by a value of type a. Therefore, if you want a family of morphisms that operate on your type t, you put it last, but if it is your type that parameterized a family of morphisms (as with regex for instance) you put it first.

If I take this two examples from the standard lib:

List.map;;
- : ('a -> 'b) -> 'a list -> 'b list = <fun>

List.nth;;
- : 'a list -> int -> 'a = <fun>

I consider the first one has a good type: we transform a morphism from a to b to a morphism from a list to b list (the type constructor list is a functor, and map is the fmap of the functor type classes in Haskell). But for the second one, I would gave it the type int -> 'a list -> 'a considering this is only a generalization of hd : 'a list -> 'a (== List.nth 1).

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