At very highly level the three areas that need to manage are scope, cost and time also known as the triple constraints.
Make sure the sponsor clearly defined the project. It is highly unlikely that the sponsor will document the scope. Therefore you need to document the scope and get some type of agreement from the sponsor. An e-mail might be a good start.
Make sure all drawings and other documents are clear with sufficient details. Recently I encountered there was a situation where specification state, use ABS (Acrylonitrile Butadiene Styrene), without any other details. These types of situations create confusion, delay, and unnecessary costs.
Make sure your sponsor, you and the vendor clearly understand the project related cost. It is good to request for quotes from multiple sources, and understand all the deliverable. Considering the current situation expect pay more than the market price. It is good idea to have about a 10% buffer.
Make sure the machine shop clearly understand the project timing. Don’t push the machine shops, they may agree to timing that they are unable to fulfill. Make an attempt to have regular communication with the vendor. This is very important.
It might be a good idea to seek recommendations from your current local machine shops.