Used packers plenty over the years in the UK and overseas and they have been nothing but professional and very efficient.
Hope you have had a good clear out so your not taking 'stuff' to the new place, just more to sort out.
But my routine tends to be the same after having a good clear out, and it makes it easier to clean as you have done each draw etc.!
I always make sure I have important documents in one folder, passports, anything of value, jewellery and the like, always take them with me separate .
Pack a box with bedding/pillows, towels, soap/toilet bag etc and either have that packed in your car or the guys pack that box last. This way as soon as you get to your new home and the beds are in the rooms you can make the beds up right away, I never leave it until later as you will be tired and not having to hunt around for this kind of stuff saves a lot of frustration.
Another box I have has the important kettle/cups/tea/coffee/drinks/some cutlery and plates, just to see you through, I usually have the toaster to hand as well with a small amount of foodstuff, bread/milk and the like, as well as toilet roll and some wipes/cleaner, again I take this with me.
I usually if moving in the UK have a change of clothes for everyone inc shoes and nightwear, unpacking clothes can be a right chore, in the car, packing cube in a suitcase are great for this.
I always make sure I empty the bins and always have a rubbish sack at the door so its easy to just pop things into. Tell the guys its a rubbish bag though or label it.
Other than that just let them get on with their job, they will go from room to room packing everything and listing on a sheet then marking each box for which room it belongs, anything specific you want them to do tell them, save any confusion and if anythings staying either mark it with a post it or walk through each room (which would normally happen) and explain if anythings to stay.
Just try and stay calm!