Ordinary construction and cleanout debris is welcome. The exclusions come from New Jersey law and from what the receiving station will take.
New Jersey makes recycling mandatory rather than optional. Each county names the materials that must be kept separate from trash, and every town writes that list into its own rules, so what counts as a recyclable in Clifton is a local answer. Your account manager can check the current list before you load.
Electronics are their own category. Televisions, computers, monitors, laptops, desktop printers, and fax machines are collected free through New Jersey's E-Cycles program and should never ride out in a container. Clifton says plainly that its crews will not take them with the garbage either.
Hazardous waste, liquids, paint, solvents, fuel, and asbestos are out of a standard container everywhere, and Clifton adds propane tanks to that list in strong terms. Tanks are the homeowner's responsibility, they will not be collected, and leaving one out can earn a summons.
The City's curbside crews also refuse dirt, stones, brick, and concrete. In a rented container those are accepted, but they are heavy, and they are the fastest way to an overage charge. Ask your account manager before you load anything you are unsure about.