If you have any non-banned items that you’re either on the fence about or know you’ll need immediately for move-in, you should pack an essentials box to be placed at the end of your moving truck for easy access. You won’t be able to do much cleaning or prep work on your new home before your movers arrive anyway.
If there is a chance you’ll arrive in your new city or town well before your belongings, you should pack your car with extra clothing and an air mattress to avoid the potential cost of an added hotel stay.