I suggest you use English File. It covers all aspects of language: grammar, vocabulary, pronunciation; as well as the four skills. There are practice exercises and many activities. I understand that you don't want to buy lots of books; but if you can get the teacher's book (even second hand online), it would be worth it.
Headway is another good option at that level. However, I think that is less well suited to a one-on-one class as there are long reading and listening exercises as the basis of language study. That sort of work could be boring in an individual lesson.
All the best,