Electronic signatures are accepted as valid signatures; moreover, even without any signature, if all the elements of a contract are found (such as the important terms: services to be rendered; cost; time, date, place; etc.) and there is evidence that the parties intended to enter into a contract for those terms, a court would typically find that there is a contract. From what you write, there is a good likelihood that you will be found to have entered into a contract for moving services.