Wood, drywall, roofing, flooring, furniture, and general cleanout junk are all fine. The short list of refusals comes from state rules and from what the receiving facility will take.
Mississippi bars a permitted landfill from accepting hazardous waste, anything with PCBs in it, free liquids, loose asbestos material, and whole tires that haven't been cut or shredded. The state rules from the Mississippi Department of Environmental Quality apply to every load that crosses the scale, no matter who hauls it.
Car batteries have their own rule. The same agency confirms that lead-acid batteries are banned from landfill disposal statewide, and the retailer who sold you the new one has to take the old one back.
Paint, solvents, fuel, motor oil, and pressurized cans stay out as well. The City's recycling program lists local drop-off points for used oil and auto batteries, and it takes up to five gallons of oil per visit at each one.
Appliances and tires are usually billed per piece instead of by weight. Tell your account manager about them when you book, and the quote will hold.