I have an enclosed trailer with nice cabinets. I keep everything I need in there and keep adding to it. Make sure you put some snacks in there. Oil filters, spare set of plugs, jets, tools. I bought a very small cheap air compressor off of Ebay, very small and light weight, noisy as can be but it does everything I need it to do. Things like that I want small lightweight and easy to move and use. If it fails or gets stolen etc it is not much.
I would get a good QUIET generator. Mine is a Champion 2000 watt inverter type. You can not hear it running and will run all day long on one fill.
I put a radio in the trailer to hear the announcer when they call us. A couple of chairs to sit in and a fan to keep cool.
I put velcro on the back of my log book and my laptop so they will not slide off my counter when going down the road.
As for a list I made a long list and put everything in the trailer.
Tie downs along the wall for air tank, fuel etc are nice to have.