TBH if you are paying movers
I would kind of ignore the garage and focus on the living areas.
Get one box for the kitchen and the bedrooms which will travel with the family
Kitchen will be the must haves to camp out untill the movers can deliver if they have to store the truck up for a day or two.
Ditto on the must have toys pillows, used bedding, and a couple of changes of clothes.
I would hold off changing the childrens bedding so their bedding smells like home for a few nights in the new house.
Then
My aim would be to only unpack items which you want to keep for the new house.
So new house map (multiple copies for the doors of each room) and number the rooms so the mover know which rooms you expect them to put stuff.
And can help you imagine the item in the room (or not).
Are they packing in one time you own the boxes or reusable crates which they need back on the day?
And rather than killing yourself have a plan to have the "crap" put into boxes to be put in your new garage so you can dispose of them when you have time.
So colour stickers of dump/recycle sell/give away/not sure items which can be packed boxes if not got rid of before hand.
If you are selling photo and list as you go.
You can get children and hubby to do their stuff
Anything not stickered goes into the crate for the agreed room.
Check the attic and outside storage for stuff which needs specialist disposal eg paint and find out where it needs to be brought and dispose safely.
Bins are they moving or staying and will they be empty in the moving day?
Enjoy your new home