Everyday house and job-site debris is fine. The limits come from Texas rules and from what the regional sites will take.
Texas keeps three things out of every landfill in the state, whatever its class: used motor oil and used oil filters, lead-acid batteries, and regulated hazardous waste. The state environmental agency lists all three as prohibited, so each one needs its own route.
Tires are restricted rather than banned. The landfill charges per tire up to 24.5 inches across and refuses loader, farm tractor, motor grader, and scraper tires altogether. Tell us if any are going in the container.
Paint, solvents, fuel, antifreeze, pool chemicals, propane tanks, and anything containing asbestos are out as well, as are liquids of any kind. McKinney households get a set number of hazardous waste and electronics collections each year through the city, which is the right route for those items.
Shingles are the local item to plan for. They aren't banned, but they trigger a surcharge, so they're worth separating. Ask your account manager how to split the load before you start.