Ordinary remodel and cleanout debris loads without trouble: framing lumber, drywall, plaster, flooring, roofing, tile, cabinets, doors, windows, furniture, carpet, and cardboard are all fine, and clean brick, block, and concrete belong in the smallest unit.
Hazardous material is firmly out, and Raytown writes it into its own rules twice. The city makes it unlawful to put banned material or hazardous waste out for normal collection, and requires hazardous waste to be handled only as federal and state rules allow. In practice that means no wet paint, solvents, thinners, fuel, motor oil, pool chemicals, pesticides, asbestos-containing material, batteries, or liquids of any kind.
Missouri also runs separate disposal rules for a few specific items, and Raytown's own code points at them: batteries, scrap tires, and some plastic containers each have their own state treatment. Keep tires and batteries out of the container and mention them when you book so they can be handled on their own.
Woody yard waste is separate as well. The duty to split limbs, brush, and leaves out and arrange their disposal falls on the property owner or occupant, so plan that as its own job rather than mixing it into a remodel load.
One more Raytown rule is worth knowing: it is an offence to put your waste into someone else's container without the owner's written consent. A shared alley container behind a business is not a shortcut.
Anything borderline, a part can of stain, an old water heater, a sealed drum, is worth a quick question to your account manager before it goes in.