Ordinary construction and cleanout debris is fine. The limits come from New Jersey's recycling law and from what the county facility will take.
New Jersey builds its rules around separating recyclables out of the disposal load. Under the State's model recycling ordinance, it's unlawful for a collector to take solid waste mixed with designated recyclable materials, and separating them is the responsibility of whoever generates the waste. Keeping those materials out of the container is part of the job here.
Electronics get their own treatment under the same rules. Computers, printers, monitors, televisions, and any display bigger than four inches across are handled as electronic waste in New Jersey rather than trash, so pull them before you load.
Nothing hazardous goes in a roll-off: paint, solvents, fuel, motor oil, pesticides, chemicals, and asbestos all stay out, and so do liquids of any kind. Tires and appliances with refrigerant need their own arrangement as well.
Locally, curbside service in Pleasantville takes no construction waste, metal, televisions, or electronics, and yard waste has to be in paper bags or cans rather than plastic. For anything you're unsure about, ask your account manager before it goes in.