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Unpack the big stuff first. Ideally the furniture first. From there go by necessities: food, dishes, toiletries, medical stuff, etc. Save books abd movie and decorative stuff for last.

Take pictures of EVERYTHING in the apartment as it is when you get there; every scratch, every stain, every cracked tile, anything that is not perfect and email the pictures to the landlord, to advise them of it and to time stamp it (so they can't say you did it as new tenants).

The place won't be as empty as it is when you first get it, so it's a good time to wipe down baseboards and cabinets and that sort of thing.

Unpacking? Just so it. It's just something that has to be done so jump in!

As for buying stuff, here's my go-to list of things people should have in an apartment:

Renter's Insurance

2 fire extinguishers (one for the kitchen and one for the bedroom. Make sure the fire alarms are in working order.

Chain lock or dead bolt that can't be accessed from the outside of the door

A decent tool kit (Vice grips, 2 screwdrivers, hammer, drill, flashlight etc.)

First aid kit

Toilet plunger

Touch up paint that matches the trim

Open the box, see where it goes, move the box to that room.

Sort all of the boxes this way.

Then you can open them in that room and set them up in that room.

Always unpack kitchen and bathroom boxes first and set those places since those two places is what you will use first.

Label the boxes before hand as to what room they're going. For example, the kitchen, bathroom, master bedroom, etc.

Make sure to separately pack the things you need on Day 1. Toiletries, a change of clothes, bath towels, hand soap, dish soap, etc. Also things like toilet plungers and fire extinguishers, since you definitely don't want to be without one.

Consider what you might need to buy new, or what is worth replacing instead of moving. For example, some cheap furniture might be worth replacing, since it probably needs to be disassembled and reassembled anyway, and it'll be the difference between a smaller truck and a bigger one. (Plus the cost of labor to move it, if applicable).

Pack a priority box. Fill it with essentials like your basic kitchen utensils so you can cook for a couple of days. Clothes for a few days in a bag/box. Bed linen so you can make your bed as soon as you get there. This will allow you to essentially start living without having to worry about where you've packed things since you have your essentials.

As you pack each room, label the box with the room and a basic description of what's inside it.

This is what I do. I've moved 11 times in the last 18 years.

Plant something from seed and see how long you can make it last. Also great time to start a brand new routine for yourself.

Not sure if your family is buying or renting. But additional move-in considerations include:

getting a locksmith out on the possession date (re-key locks if buying, May not be an option if renting),

arranging for phone/internet on that same day in case it’s not included with apartment utilities)