Don't bank on sharing anything, some people can be mean with things, and honestly I got so pissed off with my stuff going missing that I asked people to stop using it.
Buy DISTINCTIVE pots, pans, glasses, cutlery. Everyone goes to Ikea and stuff gets mixed up, try and buy stuff that looks a bit different, it stops it going missing.
Don't take a microwave or mini-fridge, most uni halls do not allow them. Particularly microwaves. A kettle and toaster are useful.
When you get there go to the Supermarket to buy some food. Really good basics to buy are pasta and sauce, if your daughter is in catered halls these are a really useful quick snack. Cereal, milk and chocolate biscuits are also great for catered.
Washing powder and fabric softner. 2 towels, flip flops for the shower and a toiletry bag. You need a duvet cover and duvet. I would also recommend pillows and a throw to make the room more homely.
Laptops are well worth it (uni computers are invariably busy or crap, and when you are finishing an essay at 4am its nice to do it in your room) I would seriously look into renting one, often the union organises this. I would say well over 75% of people in my halls had computers.