When I moved into a shared apartment, for Uni, I gathered a box of stuff under my bed (at home, over the 2 months before I left):
This was an apartment where there was crockery (1 plate, mug, bowl, drinking glass, knife, fork, soup spoon, teaspoon each) and cooking utensils (3 pots between 5 of us, a pan, and very basic kitchen utensils).
2 distinctive mugs
1 decent large glass for cold drinks/beer - distinctive is good
A pasta "bowl" type dish
A small sharp knife
A wooden spoon
A grater
A corkscrew
A tin opener
A small pan
A big pan for stir-fry type dishes
A baking tray (a couple of actual baking things but mostly for pizza, waffles, the odd roast chicken leg etc)
Washup brush
A pair of oven gloves
3 tea towels and a hand towel
Roll tin foil
Roll cling film
Pack j cloths
Small salt and pepper mills (full)
Herbs and spices (I used things like basil, oregano, thyme and rosemary a lot, mild and medium curry powder - chilli powder is also very useful although I wasn't big on that back then)
Stock cubes
Cornflour (for making sauces)
Jar mayonnaise (I was a demon for bacon sambos with mayo!)
Bottle vinegar (I used wine vinegar as it was ok for chips and for salads/cooking)
Oil (I used olive even back then as again, salads and cooking uses)
Bag pasta
Bag rice
Tinned tomatoes
Teabags
Coffee
(I didn't use sugar, and wasn't a hot choc or similar drinker)
Washup liquid
Bottle kitchen cleaner
Pot scrubber thing
Bleach
Roll of black sacks
I was reasonable in the kitchen even then, so I generally cooked a fair bit from scratch.
Others in the flat were less good, so there were lots of packets of curry sauce, tins of beans, jars of pasta sauce etc.
What is your DS capable of? Would he be a cook at all? Would he like flour for pancakes, sauces, soups and even baking? Or is he a "everything from a packet straight to the oven" man?
Also, for his own room (and check what's already in it) things like a bedside lamp,
lamp for study space,
bookcase,
magazine racks to organize book spaces by subject/project (and minimize space needed by keeping papers upright!).
Bedroom bin (for rubbish and scrumpled up paper!)
Alarm clock (with radio etc)
at least 2 decent large towels for showers (a dressing gown may be useful but storage may not be there for that - large towels to wrap around are good).
His own pillows and duvet, sheets (2 sets of sheets - 1 for washing, 1 to wear)
Bag for carrying laundry, popup laundry basket could be useful if space allows
Hanging "shelves" to put into a wardrobe may be useful to get more useable space, or stackable plastic tubs