Hi David,
Welcome to the HVAC Group!
The tools which you listed are very good and what I would choose to get started. It is good to get your tools early in the course, even if it is one tool at a time. By the end of the course you will have obtained a good supply of tools and ready to be a quality craftsman.
Testing and balancing is great to know and it always involves writing everything down. It is also important to have complete knowledge of the system. There are two categories to this type of work. First to gather the necessary information and prepare forms on which to record the test results. Next, inspect the installation to be certain everything is safe for start-up.
Give the system a thorough visual inspection. make sure all ducts are complete, al air outlets are installed and dampers in the ductwork are open. Place the supply air fan into operation next but check several other things first like foreign mater, debris that could be later drawn into the fan and cause damage. Fan blade free of rotation, alignment, tension, and lubrication. The electrical supply should be checked out, recording motor nameplate data and then checking overload protection for size, and measuring voltage. With correct voltage at the motor, we can momentarily bump the fan to check the rotation. With rotation in the proper direction, the fan can be started and allowed to come up to speed, immediately following which we should measure the motor current. If actual current is less than motor nameplate rating, the fan can remain in operation.
Good Luck with your studies and tools!