We have moved a few times, most recently last year during the first lockdown.
The things we did that we were the most grateful for were the kids each having their own backpack, I filled it with things to do (colouring book and pencils, their tablets which I loaded up with films and books with the chargers and headphones and a new small lego set), their stuffed animal of choice and a spare set of clothes. I packed another backpack with a second spare outfit each for them and pyjamas because they have accidents. Then I added a box of snacks and their water bottles with their sleeping bags, we set them up a safe space where no boxes would be put and they could stay out of the way. That way if we didn't get their beds up they still had somewhere warm to sleep. To be fair they have additional needs and I pack quite a lot of that for a day out anyway, they don't like change and it makes them feel safe.
The essentials box: kettle, mugs, plastic plates and cups for the kids, teaspoons, coffee, sugar, tea, milk, squash, biscuits, teatowels, scissors, tin opener, veg peeler, toilet rolls, bin bags, lightbulbs, torch, packing tape, the first aid kit, baby wipes, sanitary towels, painkillers and a spare phone charger. Washing up liquid and handwash were also useful but easier to run to the corner shop for and for us not worth the risk of leaking. We were very glad for the box since it took a few days to have a working heating system and have the cooker delivered.
and the paperwork folder, everyone's important documents already lived in a small folder, I added that to a bigger one with all the house paperwork tenancy agreement. I added the list of everyone I needed to call to update the address details. I actually tried to change a lot of it as soon as we got the new address.
The list of places you need to call and update your details is personal and different for everyone but a good starting point
Utilities - Electric, Gas, Water, Phone (mobile and landline), Broadband, TV license, Bank accounts and Credit cards if they are different and the kids schools.
Services - Doctors, Dentist, Opticians, NHS if you have hospital appointments or a pre-payment card for prescriptions, HMRC if you receive benefits, Amazon, Ebay, Whatever your takeaway of choice app is Deliveroo, Just Eat etc (because trust me it really sucks when they deliver your Chinese to the old house and then call to ask why nobody is in and it would suck even more if they delivered it to new occupants) and all your reward cards e.g Tesco, Sainsburys, Waitrose because they can't send you vouchers if they have the wrong address. Make a note of anywhere else you order from regularly like clothing retailers, plus any subscriptions you usually have delivered for us this was the kid's magazines.
Good luck, don't forget no matter how chaotic it looks it is temporary.