Most remodeling and cleanout debris is fine. Idaho leaves most item rules to the counties, so Teton County's list is the one that counts in Victor.
The Idaho Department of Environmental Quality says burning household trash, dumping on public land, or disposing of waste at an unapproved site is illegal. Beyond that, the state points residents to their county landfill for electronics and hazardous household items.
Teton County does not accept household hazardous waste. That includes paint, antifreeze, brake fluid, cleaners, glues, aerosols, pesticides, and anything containing asbestos. The county will pay back residents up to $150 a year for taking those items to the hazardous waste site in Teton County, Wyoming.
A few other county rules help with planning. Old tube TVs and tube monitors count as household trash, while flat screens go to recycling. All Styrofoam is treated as household trash. Liquids, solvents, and fuel can't go in a standard dumpster either, and tires and refrigerant appliances cost extra, so mention them when you book.
Your account manager can check any item you're unsure about before it goes in.