Usually I do all the standard stuff: Viscosity curve, shot to shot repeatability, cavity balance, gate freeze, cosmetic window study, cooling time study, and a DOE if needed. I also check the water flow and water temp through the mold using a flowmeter, get steel temps, and melt temps. I have gotten demolding temps in the past as well. I also record outputs like fill time, peak pressure, cushion, end of fill weights, and part weights. I dumb all this information into a online program we use so all the other engineers can find it if needed. We do document the inputs as well in a setup sheet. I am sure I forgot something in the quick response. Look up on Suha's website. His book is really good and has a lot about testing, documentation, and building a robust process. Would be a good read for you if you are trying to set up something.

Also our tool room documents a lot of stuff on the tool when it comes in. Like venting, gate size, etc. and then they put that in a file for the tool.

Good luck!