Most remodeling, roofing, and cleanout debris can go in your container. The limits come from South Carolina's landfill rules and from the county landfill that takes the load.
State law keeps used motor oil out of landfills and household trash. It also bans computers, monitors, and TVs from regular trash, and landfills aren't allowed to knowingly take a load that includes them. A single TV tossed in with your debris can cause trouble at the gate, so pull electronics out first.
Standard exclusions also apply. Keep hazardous waste, liquids, paint that's still wet, solvents, fuel, and asbestos out of the container.
The Oconee County Solid Waste page lists what the Seneca C&D Landfill won't accept. That list includes household trash, electronics, cardboard, metal, liquids, friable asbestos, PCBs, and anything that's been in contact with petroleum, pesticides, or solvents. Non-friable asbestos needs a state disposal permit and extra fees. Used oil, car batteries, and old appliances can go to the county recycling centers instead.
When you're not sure about an item, ask your account manager before it goes in.