Residential Dumpster Rental isn't a smaller version of a standard rental. It is a container scaled to a house and a driveway rather than to a job site, and that's what you're actually paying for. Carry this into the conversation: where the box sits, and what it sits on, causes more trouble on residential jobs than the size ever does.
The box has a size and a separate weight cap, and it's the cap, not the size, that decides whether you owe more at pickup. Ask around and you'll find homeowners renting for this more than anyone else, choosing from containers as large as 10 or 15 or 20 yards. The booking is short once you know the weight of the load and the length of time you need the container on-site.
Furniture and mattresses take up space without much weight behind them, so the container runs out of room long before it comes close to its hauling limit. Ask what happens to a container that sits mostly empty -- some yards pick up early and adjust the bill, others hold to the full rental period regardless of how much got loaded. Order the size you can defend, not the size that feels safe. That's the decision in front of you.