One thing I would add to this list if you are going to carry things for emergencies is to carry some rope and bungy cords with you. There may be times where you pick up a trailer and the chains/hooks that hold the trailer doors open are gone or broke. You will need some way to keep the doors opened properly.
As a company driver, I wouldn't worry too much about the tools, so don't end up carrying a big tool box or anything. Just the few basics for very minor roadside emergencies. If you end up having to actually make big repairs on the road yourself, then it is time to find another company
