Standard construction and cleanout debris is accepted: lumber, drywall, roofing, flooring, cabinets, doors, windows, fixtures, furniture and general household material.
Nothing hazardous belongs in a standard container, nor do liquids, paint, solvents, fuel or asbestos. In Oro Valley it is worth adding pool chemicals to that list, because chlorine, acid and pool stabilizer are common in an Oro Valley garage cleanout and none of them belongs in a container.
Arizona law governs the load once it is on the road, and it is written tightly. A vehicle may not be driven unless it is constructed or loaded to prevent any part of the load from dropping, sifting, leaking or escaping, and the load and any covering must be securely fastened so neither can come loose or become a hazard to other road users. A first violation in a sixty-month period that causes no damage or injury carries a civil penalty of up to $250, rising to $350 for a second or subsequent violation.
That rule is the practical reason a loaded container is tarped and why we will not take a load heaped above the rails. It also matters for a desert landscaping job, where light material such as palm frond and dry brush will lift straight out of an uncovered container at highway speed.
Tires, appliances and electronics are normally priced by the piece rather than by the ton, so set them apart and declare them at booking.
If a single material is the open question on your job, ask your account manager before it goes in rather than after.