A dishwasher/dryer they’re pretty essential or a rotary dryer

I would first make an inventory of what you already have. And start from there.
What in my idea is absolutely necessary is a washing machine.

Cleaning supplies, tissues, cloths, tea towels then your basic plates etc because you will get hungry moving!

Hard question to answer without knowing what you already have and in what context. Things like batteries, scissors aren’t really something you think of but need when moving in.

Things such as baking paper, glad wrap and sandwich bags. Garbage bags. Extension cords.

This is a hard one to answer without knowing what you already have or if you’re moving in with nothing. Quite often I’ve found you don’t think of things until you’ve moved in and realised “Oh, I could really use one of them right now!” Good luck with it all, exciting times moving into a new house

Luckily before we moved into our home we had the basics.
It will be items such as curtains and they can be expensive and best bought on sale.
It is a good idea to go around your current home and take an inventory and match up with your new home. If your new home does not have it and you need or want it add it to the list. This might be the best way to figure out what you need.

Make a list of what you use all the time. List furniture you’ll need right away like bed, lounge, tv etc whatever is essential for you and save all the little things and personal touches for once you’re settled and get a feel for your home you’ll be able to source what you really love and give your place longevity.