Nice job! As a US-based consultant, I've found it's always best if you immediately suggest a contract. This way you can ensure it starts with terms favorable for you.

I've also found it's pedagogically helpful to have two versions of each contract, a consultant-favored and consultee-favored. This way you can understand how each clause may be tweaked to benefit each party. For example, this book does this (US-based): https://www.amazon.com/Consultant-Independent-Contractor-Agr...