Buying a tow truck

To answer your question - it will depend on the truck itself whether you'll need a CDL. I think you could get up to a 4500 size without one so you wouldn't need one for the C30. But if all you intend to use it for is scrapping vehicles, I'd suggest a tilt trailer with a winch. Cheaper to purchase, license, maintain and more flexible for using.

I know over here that most of the "smaller" operations with tow trucks got rid of them because the insurance got so high.
I would get a quote from your ins. company first to see if you can afford it. If your an independent then I don't think you would need a license. Maybe just a county permit.

As far as insurance on the truck, it'd just be regular liability insurance. Just put a sign in the window "Not for Hire". Otherwise, your liability is sky high plus there'd be what's called "on hook". When I looked into it, it'd cost approx $2,000/mo. The problem will be when the insurance company requires "Business Insurance" and classifies you as a scrap metal dealer (think: stuff blowing off your truck and hitting someone). I don't know what you're insured for now but most people doing this aren't insured for hauling scrap metal.