I'd probably start with a basic circular bowl(er) shape; just the head part, because it will be easier to fit it to the head and extrude the brim afterwards, I think. Even half a sphere would give you a good starting point for pulling and pushing; or better, a quarter sphere. Once you have it shaped to one half of the head, mirror and join. For the trilby morphs you may want to cut your mesh so that the morphs will form easily without bumpy edges.