Boxes - ask stores, esp the likes of Wickes, Homebase etc if you can have boxes. You need to sort this in advance because many stores bale and shift their boxes as soon as they unpack them. If you pay a firm to move you, they may provide boxes, wrap, tape etc as included or extra. If you pay them to pack, they provide everything.
Give the movers a floor plan and label doors in new house. They will assume everything in Bed 1 in the old house goes in Bed 1 in the new, but you can stick a note on anything that needs to go in a different room so that they can pack and unpack as you want. Agree amongst yourselves first so movers get clear instructions.
We've 'upsized' and 'downsized' but in both cases, clearing out what you don't need is sensible. It is mad to pay someone to move clutter and even madder to store it in another home.
Measure doorways/windows and identify any furniture that won't fit. Sell what you can and give away the rest. As well as Freecycle, a lot of towns have local for sale/wanted/free if you collect pages on Facebook. Good for boxes and for selling what you don't need.
Take your essentials box (kettle, mugs, coffee, snacks, plasters, scissors, aspirin, door wedges, loo roll, soap, a hand towel, cloths, washing up liquid etc) in the car with you. I would also keep a suitcase of your bedding, towels and a bottle of wine in the car so you can easily find them.
Plan your food for the day, especially if eating out isn't an option.