Best advice, each person will take different things but if you have a look at each room and go off what they use now, so bedroom, definitely a mattress topper/protector, bedding, pillow etc any toiletries they keep in there, hairbrush, deodorant. Clothing, coats, shoes, hats, gloves, scarf.
Then bathroom, tweezers, nail clippers, razor, plus shampoo etc and wherever you keep your medicine kit, they need those things too.
Desk stuff or wherever they do their homework, laptop, pencil case, chargers etc and a bag to carry it all in.
Kitchen, chopping board, knife, cutlery, crockery, pans. The main thing to consider is the shared kitchen cupboard space. Ds had one 50cm base unit for kitchen utensils/pans/crockery and a 50m wall cupboard for all his food. Lots of food lived in his room. We bought a saucepan with a draining lid (Lakeland) so he didn't need a colander or sieve for pasta or veg. He had 1 frying pan, 2 plates in case he broke one, one pasta bowl, one cereal bowl. 2 each of knife, fork, spoon, teaspoon. Some tupperware to store opened things like packets of sandwich meat or leftovers.
He had a Dishmatic washing up brush which was stored in a mug in his cupboard. They do not have a lot of room and YouTube has lots of room tours of unis plus their kitchen space.
Good to watch people saying this is what I am taking, then the year later video of them saying never used this. Ds never took a grater or garlic press as he bought grated cheese and squeezy garlic tubes.
Check the uni policy on what they can have in the kitchen electrical appliance wise some unis are very strict on things see also their room, they can't have kettles or fridges in lots of places, check before you buy.
All of this stuff has to be able to fit into whatever car you have too, so it is all well and good saying pack all this if they only have a Fiesta with 2 adults and the child piling in to it as well. Again, YouTube has lots of moving in videos, well worth a watch. Best of luck.