Most household and building debris can go in your container. The limits come from Texas rules and from the landfill that takes Longview's loads.
The City's landfill page lists several things the landfill won't take. Tires are refused unless they're split, quartered, or shredded. Oil, oil filters, and lead-acid batteries are not accepted. Refrigerators, air conditioners, and other appliances with refrigerant are taken only after a certified technician removes it, and you'll need the certification letter.
Electronics follow a looser rule in Texas. The Texas Commission on Environmental Quality says most household hazardous waste, including electronics, can go in your regular trash. Businesses have to check first whether their electronics count as hazardous.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster. If you're unsure about something, ask your account manager before you load it.