Yes get an engagement letter/agreement signed before you start work. In addition to what StrongSilence said, your professional liability insurance carrier probably has them, too.

He left the prior CPA bc he didn't like the fees.

I agree with the others - I prefer not to do this quarterly calculation crap for a small business. I have them pay safe harbor estimates. They can tell me if anything major changes. If I do end up doing the quarterly work, I'll charge at least what Phoebe said.