Most of what comes out of a remodel is fine: lumber, drywall, roofing, flooring, cabinets, fixtures, furniture and general household junk all load normally.
The hard limits are hazardous material and liquids. Paint, solvents, fuel, used oil, pesticides, car batteries and asbestos all have to stay out, and so does anything still holding refrigerant. Hazelwood also makes it an offense to burn debris on site unless an approved incinerator or an air-quality variance is in place, so a container is the practical route for everything you clear.
Tires, appliances and electronics are billed separately at most receiving sites rather than banned outright, so tell us about them when you book and we will quote them properly instead of letting them turn into an overage.
Anything you are unsure about, raise it with your account manager before it goes in. One wrong item can get a whole load rejected at the gate, which costs far more than handling it separately.