Normal house and jobsite debris is welcome. The limits come from what the city will not collect and what the receiving facility will not take.
Start with the city. Portage's contracted cart service does not accept construction waste, auto parts, tires, household hazardous waste such as paint, oil and cleaners, or medical and electronic waste. Free bulk pickup exists but is limited to one item a week, which does not cover a remodel.
Hazardous waste, liquids, paint, solvents, fuel, used oil, batteries and asbestos stay out of any container. Those belong at the Kalamazoo County Household Hazardous Waste Center, which is free to Kalamazoo County residents outside Climax Township and takes oil-based paint, pesticides, batteries and electronics including laptops and televisions.
Tires and appliances need their own arrangement as well, so mention them when you book rather than after the container is loaded.
One item deserves extra care in Portage. Many homes here date from the 1950s through the 1970s, so have older flooring, siding and pipe insulation checked for asbestos before demolition starts. If you are unsure about a material, ask your account manager before it goes in the container.