Lumber, drywall, roofing, cabinets, flooring, furniture, and ordinary cleanout debris all load without issue. The short refusal list comes from Virginia rules and from the receiving facility.
Car batteries are flatly banned. The Virginia Waste Management Board prohibits putting a used lead-acid battery into mixed municipal solid waste, and state law treats every battery discarded that way as its own violation. They go back to a retailer, a wholesaler, or an authorized recycler instead.
Hazardous waste, free liquids, paint, solvents, fuel, motor oil, and asbestos stay out of every container. The City's own collection rules say the same thing for household trash: no paint, oil, hot ashes, or hazardous material.
Screens and tires need their own route. Virginia lets a locality bar televisions and monitors from local disposal sites when it runs a recycling program for them, and the regional authority operates a tire processing facility rather than burying tires. Take both out of the load before pickup.
Appliances holding refrigerant, mattresses, and tires are generally billed per item. Tell your account manager about them when you book and the quote will hold.