We learnt the hard way with DS1 not to take a massive plastic box! This was his father's contribution to him starting uni and it was filled with store cupboard staples. It was huge and very heavy and took up loads of space in his wardrobe. At Christmas, I took it home and it now lives in my shed. I'd bought collapsible crates for him, but actually, they were small enough to be stored under his bed still set up, so he kept quite a bit of his store cupboard food in them.
For DS3 this year we have some collapsible crates, some fabric covered cardboard cubes and some blue Ikea bags and their big zipped bags for duvet/pillows etc. So the pretty cubes can either be folded down or put on shelves or in the wardrobe if space, the crates folded down or left up if they fit under the bed. He's also got two suitcases, a medium sized one for coming home at Christmas on the train and a cabin sized one in case he ever gets to go abroad, which fits inside the bigger one. I'm hoping they'll both fit under the bed.