Editing would probably be the best way to break into the business if you are serious about doing so. Directing and screenwriting are incredibly difficult to make it in as they are highly competitive fields and more dog-eat-dog than editing would be, which you could most assuredly find a place to be.

Ultimately, you could still direct and do some screenwriting without having much of an educational background. A lot would make it easier, but I do not believe it is an absolute requirement.