New Wellness Center Director; what type of contract/agreement should be signed by outside trainer/instructor?

I would consult an attorney. It may cost you a little bit of money. But if you don’t get it right and something goes wrong, it could cost you a lot of money. You could also consult other wellness centers in your area. They may have a contract that you could use as a template and insert your information into for an attorney to go over for you. Contracts are not trivial matters.