I think OP mentioned that it was a long-term rental property that they were moving into? Hopefully it will be clean and well-maintained prior to move-in (by the landlord).
@OptimisticReindeer Do leave enough time in your schedule to thoroughly go round the house in the first day (before your stuff is moved in), and check that you agree with the inventory (ie the condition of everything that is in the house). I think you only get approx a week to challenge anything. Take photos of things that you feel need to be amended on the inventory, and note it all down in an email.
When moving, I have found it works best if you really plan where and how things are going to be stored at the new place, before you move in. So then you don’t need to spend ages deciding, or working out how to make each room work, when what you need to be doing is unpacking really fast.
So I will plan out where everything goes in the kitchen (take photos of the new kitchen to help you plan). And on moving in day, I will put post-it notes on all the drawers and cupboards in the new kitchen to identify what will go where, so that it is really quick to unpack, and if someone is helping you then they know where to put everything.
I also work out where furniture will live (and draw a plan of the room with proposed furniture locations in, so that things can be placed in exactly the correct place). I also work out beforehand if any new storage furniture is needed and try and get that beforehand.
The last few times we have moved, we got the removals company to pack, and also to dismantle and re-build things like beds and wardrobes - that really helps save time, especially if they can re-build them into the correct location. They bring clothes on hanging rails during the move, so they can go straight into the wardrobes that they have built.
I also organised our things before the move - so, a trip to ikea to get lots of drawer dividers and storage boxes (that will be used on an ongoing basis) - it becomes really easy to just unpack a box that contains clear storage boxes full of things in, that then just lives on a shelf in the utility room, for example. (So I have shelves in my utility room and they are full of small, clear plastic boxes - for example, one with sewing kit and ribbons and buttons etc, one with a whole load of different greetings cards, one with shoe cleaners / polish and insoles, one with pens/pencils and school equipment). It makes life so much easier when you move if everything has been planned and organised!