Fixed price all the way. Time and materials contract will spiral out of control fast. Unless you can financially incentivise the project manager to meet targets. say basic weekly wage for PM and then a bonus for meeting targets like meeting cost, time and quality targets. I don’t know how you would set such targets without professional advice from a QS. Be very careful not to allow contractor/PM to load payments towards the early payment.
I have seen some horror stories Where PM has been given too much scope basically stealing materials and defrauding his client. Don't do it unless you are actively involved and very careful and remain suspicious/vigilant