Get multiple quotes from various fabricators to find the best deal for your project. In order to provide a PCB assembly quote, they will need a few pieces information from you. Make sure to get these ready before initiating your orders.
For example, they will ask for the Bill of Materials so that they can estimate the cost of the parts. You should also provide them with the assembly drawing, the fabrication drawing, the ODB++ files, and the Gerber files. If these are unfamiliar to you, then discuss the matter with your head of engineering.
Put all of these in a ZIP file and send it over to the companies. If you are still in the process of getting the files ready, then you can try to talk to the PCB assembly candidates to gain insight about costs. They could set expectations and provide clarifications.