I think the answer is very different depending on both what your DD is like and the split between parent/student 'must haves'.
When I was at uni, the only thing I bought myself for my room was a drip-coffee machine - it was a bargain and so nice to be able to have a coffee without going to the kitchen.
There's very little storage so I could have done with some of the hanging storage you add to wardrobes but other than that you just cram all your clothes in and then everything else goes under the bed!
Agree with mattress topper being lovely and very obvious utensils are handy (I went with green handles so easy to see). Nothing too nice, as things as well as food will go missing from communal kitchens!
I also just used a large bag for life to transport my washing as you can fold it up.
A nice purchase is loads of notepads if they'll be taking paper notes as it sucks spending money on paper when you want to go out!
From a student pov must haves are: Pack of cards, fancy dress basics like a set of face/body paints, interesting art for your walls, any stuff youll need for societies (e.g. swimming costume/shin pads/hiking boots), lots of snacks to share with housemates and alcohol. You'll get about 80 bottle openers and pens during fresher fairs.
The best purchase in my first year was one of my housemates getting a hamster that we all took turns hiding during inspections!