Most construction and cleanout debris is welcome. The exclusions are the usual ones, with a few local details that are worth knowing before you start loading.
Hazardous waste, liquids, solvents, fuel, used oil and asbestos all stay out of a standard container. So do propane cylinders, ammunition and sharps. Tires have to be handled on their own, and they are refused even at the regional household hazardous waste site, so plan a separate route for them.
Paint is the one that catches people out, and the rule is a useful one. Oil-based paints and stains are hazardous waste and need the facility below. Latex paint is not hazardous once it has completely dried out, so you can take the lid off, let it harden or stir in cat litter or sawdust, and put the dried can in the trash with the lid off so the driver can see it is dry.
Yard waste is also separate here. Village collection takes it only in biodegradable bags, and no bag may weigh more than 50 pounds, which makes a container the practical answer for a big brush job.
Anything you are unsure about is a one-minute conversation with your account manager before it goes in.