Lumber, drywall, shingles, flooring, cabinets, siding, fencing, and general cleanout junk all load fine. The limits come from Texas rules and from what the receiving landfill accepts.
Texas prohibits four things from every class of municipal landfill: used oil, used oil filters, lead acid batteries, and regulated hazardous waste. Untreated medical waste is barred as well, outside a declared disaster. Asbestos containing material is a special waste with its own handling rules and has to be covered as soon as it arrives, so it needs to be declared before anything is loaded.
Beyond the state list, hazardous waste, liquids, paint, solvents, and fuel stay out of a standard container. Refrigerators, freezers, and refrigerated window units are worth calling out, because the city landfills will not take them at all.
Residents can drop used oil, antifreeze, and oil filters at a city convenience station, and paint and other household chemicals go to the Southside station on 84th Street. Ask your account manager before putting a questionable item in the container.