They do everything! Check also that they will re-assemble anything that they take apart to pack - especially your beds. Ask what they do about wardrobes - they may bring temporary cardboard wardrobes to put your clothes in. I packed my small personal valuable items, and carried those with me in the car. Check that they are insured for breakages of stuff they pack.
Best to have had a good tidy and sort out, and to label boxes as they go - label them with contents and the room in new house you want them put in when they unload.
They pack v v fast, and not always logically - bathroom products in a box with pet food - that sort of thing!
We've had full packing twice, and I think it is well worth it.
They will come and collect the big stack of empty boxes a week or so after you have moved in - ask them about this.
They will probably want to come round and have a quick look around your home to work out how big a job it is. What they will and won't carry varies from company to company. I have had companies that will take everything to companies that won't take items such as paint, alcohol, paintings of value so it's worth reading their small print on your quote. I have moved 5 times (including abroad and back) in the last 10 years and have used a packing service each time.
The only things ours wouldn't do is paint, barbeque gas bottle, and camping gas. Everything else went.
We've done full pack twice, and they were brilliant. If you are on your own with a LO, they will undoubtedly do everything they can.
Just make sure you have clothes, shoes, sleeping bags/ travel cot and some crockery/kives and forks in the car out of the way cos they pack everything and its nice to get to new house and know you can get a takeaway, eat it and then sleep without needing to unpack
I've had a full packing service once and it was fab! They wouldn't take paint but that was all. I put the hoover in my car, so I could run it (the hoover, not the car!) over the old house quickly once it was empty so the dustbunnies didn't get left behind for the new people. I also packed most of our clothes into suitcases as we were leaving the fitted bedroom furniture behind (obv!) and didn't yet have new furniture in the new house.
Make sure you have chocolate biscuits for them - the two guys that packed our house were the leanest, wiriest looking chaps you ever did see, but they ran on chocolate biscuits and sugary builder's tea