Most renovation and cleanout debris can go straight in. The limits come from New Jersey's rules and from what the county landfill will take at the scales.
New Jersey keeps covered electronic devices out of the trash. Computers, monitors, laptops, televisions, and desktop printers and fax machines go to electronics recycling instead. The state also requires recyclables to be separated where they are created rather than picked out of a mixed pile later, and Long Branch makes that a duty of every owner, tenant, and occupant.
Hazardous waste, liquids, paint, solvents, fuel, and pressurized tanks stay out of a standard container. The City's own list of household hazardous waste names wet paint, lawn and garden chemicals, household cleaners, gasoline, motor oil, antifreeze, mercury thermostat switches, and batteries. The county runs a separate drop-off for those at the same Tinton Falls site.
Asbestos has its own track. The county will only take it bagged and labeled under a separate waste code and at a higher rate, so test older roofing, siding, and flooring before you tear them out.
Two city rules about the container itself are worth noting: it must not leak liquids or solids into the sewer system, and it has to be emptied once the load reaches the container's waterline. If an item has you guessing, ask your account manager before it goes in.