Ordinary construction and cleanout debris is exactly what these containers are for. The limits come from what the city refuses and what the receiving site will take.
Start with the city, because the list is blunt. Gulfport's curbside service will not pick up building material, hazardous material, tires, broken concrete, or any debris created by a contractor. Its debris crews will not take hazardous waste, mattresses and furniture, tires and engine parts, home appliances, or contractor and commercial debris.
The code adds more to the list of things that have to be carried to a city site instead of left at the curb: refrigerators, freezers and other appliances holding refrigerant gas, anything with PCB capacitors or mercury switches, televisions and other electronics, motors, vehicles, boats, and anything unusually large or heavy.
So hazardous waste, liquids, paint, solvents, fuel, used oil and asbestos all stay out of your container. Household chemicals belong at the county collection site on Lorraine Road, and tires need their own arrangement.
One coastal note worth adding: after flooding, treated lumber, insulation and anything contaminated can be handled differently from clean debris, so tell your account manager what the load actually is before it is built.