I never submit a PO for boards before having a stackup approved by the vendor, including a document which includes substrate material definitions, copper thicknesses, and imedance requirements (if any).
The next time I need that stackup with that vendor, I'll just cite the original stackup specification. If I change vendors, I start the process over.
The only exception is when I'm doing something very basic where impedance and current handling aren't very important. In such cases I'll let the vendor decide which of their "standard" stackups to use.