You're asking some really big questions, especially considering the extent of the project as you've described it.

I think the first thing for your family to consider is what they want to do with the house and all of it's objects. Do you want to sell them, keep them, donate them to a museum, or turn the house into a museum.

Just some basic tips while you are creating the inventory:

Make sure that if there is any family history associated with an object, write it down. An items history would be important for a museum interpreting the object, and for providing provenance.

I also might recommend getting some collections management software if you haven't. If you don't mind spending some money, I would recommend PastPerfect. If you are looking for a model which is somewhat on the more free side, I'd take a look at the opensource CollectionSpace. It was demo'd at a conference I attended, and I was impressed.

In terms of handling, don't try to clean anything yourselves until you educate yourselves. I'd start with these short videos about historic home housekeeping which goes into appropriate methods. It's a bit dated, but it's still a pretty good resource.

Another few basic handling rules:

Only carry one thing at a time.

Lift an object where it is most structurally stable, which is often not where an item was originally meant to be held. This means don't carry a pitcher by the handle, but by one hand on the bottom and one hand on the side.

A cheap box of nitrile gloves can be your best friend when handling artifacts. They make sure that your hands don't damage the objects, and that your hands have at least some protection if they run into something icky. The purple also makes a daring fashion statement.

Lastly, I'd recommend you think about inviting a few staff members of local museums over, probably curators, directors, and collections managers, and a few historic preservationists if you could swing it. They would be able to give you more immediate advice about care and what historical interest the house and it's objects may hold. The historic preservationists might be able to tell if any part of the house's structure or pieces is in immediate danger. If you ever do decide to donate the items, or turn the place into a museum, some input from local museum and preservation professionals would be invaluable.

Just let me know if you've got any more specific questions! It sounds like a fun project.