All right, lots of partially correct answers here. Let me take a crack at it.
You have to follow state laws. That means, over 26,000 gross or a combination vehicle towing over 10,000 lbs, you need a CDL.
There is no rule, anywhere, that states that you need a CDL to operate a vehicle with air brakes.
If you are over 26,000, in-state, you need CDL, plus you need to comply with Hours of Service, I.E. logbooks. You do NOT need a medical card if you are intra-state only (and you self-designate your license limited to being intra-state).
You also have to follow Federal law. If you are driving for a business purpose across state lines, and you are over 10,000 gross you are a commercial vehicle for purposes of federal regulation. That means you must comply with hours of service, pre-employment and random drug testing (if over 26,000) have a DOT number (and MC number if hauling for hire), file an MCS 150, UCR filing, Heavy Vehicle use tax (if over 50,000 gross, IIRC), and comply with IFTA regulations (most states over 26,000, some, like Arizona and Nevada over 10,000). Also have to have cargo insurance on file if hauling for hire. You must also comply with all the DOT registration requirements, including maintenance, driver qualification files, Hours of service, and more.
If you have a need to travel out of state in your commercial vehicle, best thing is to find a compliance company that will handle your filings and compliance to keep you out of trouble.
"NOT FOR HIRE" is completely meaningless. None of my trucks are for hire, and I still have to comply with all the list of requirements.