The order that actually works
Pull documents, photos, and anything with a serial number before anything else moves — these are what people throw out and can't replace. Then work room by room rather than category by category; a finished room is visible progress, which matters when the volume feels endless.
What to set aside, not throw out, until someone decides
Anything that looks worthless but might not be. Firearms, which have their own legal disposal process. Prescription medication, which a pharmacy takes back rather than a bin. When in doubt, one corner of one room, decided later.
When to call in a professional cleanout service
Volume beyond a few weekends of family time, health and safety concerns (mould, pests, structural clutter), or simple distance from family are all good reasons to get two quotes from a vetted local cleanout company rather than treating this as a moral test of the family's effort.