The code
x = 5
will produce a variable x of type Int.
Generally it will be safe to write code like
foo(maxiter::Int = 1000) = for i=1:maxiter do_stuff() end
It would be somewhat overkill to define foo(maxiter::Integer) as Julia will generate not only the method foo(::Int), but also foo(::Int8), foo(::BigInt) and so on for each subtype of Integer. In this particular example, one would not expect any of these other methods to ever be used.
If your code needs to assume something about the size of the integer, go with Int32 or Int64 instead.