We just did this Fall 2016.
Small bottle of dish washing soap (Dawn works well for dishes and to scrub out stains).

Laundry pods (easier to transport up and down stairs than laundry powder/liquids).
Dryer sheets.
A few clothes pins – for whatever, clothes or to keep the opened chip bag closed.
Laundry bags. Daughter likes this one (has shoulder straps) and this one.
https://smile.amazon.com/gp/product/B014KSWKSM/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1
https://smile.amazon.com/gp/product/B001QD40R4/ref=oh_aui_detailpage_o03_s01?ie=UTF8&psc=1
Hangers.
Lots of medium and small storage boxes for under the bed. (not much storage for clothes in our daughter’s room). Sarah bought a variety of pretty boxes to stack under the bed.
Fan (one powerful enough to cool the area without being too big for space). Sarah said the “desk fan” does not keep her cool at night but works well for when she is at her desk - so she has two.
Power strip.
Emergency lantern or flashlight (with batteries). This one is good – and small.
https://smile.amazon.com/LiteXpress...=1490376748&sr=1-2&keywords=supernova+lantern
“Real” folks/spoons/knifes (bought from Target, cheap). A couple of coffee/tea cups for hot drinks.
A couple of "water" glasses/bottles.
Paper plates/bowls (easier to take care of than “real” ones, no leftover food sitting around).
Plastic wrap and ziplock type storage bags.
Electric tea kettle. (for tea, cocoa, etc)
XL sheets and comforter.
Towels and washcloths.
Surprisingly our daughter wanted a small vacuum cleaner and step ladder for her room.
A few basic tools (hammer, screwdriver, pliers, scissors).
Removable hanger hooks (like Command brand) to hang fun stuff on walls.
***Since our daughter has to take meds, we included a small safe and a bike lock to attach it to the rail of her bed so it would not walk. She also keeps her extra cash in the safe but mainly it is for her medicine. I also have our daughter on one of my credit cards so she can use it in an emergency (has to call me first so I can “unfreeze” the card). She keeps the credit card in the safe also.
***Insurance card and discuss with your child what to do if they need to go to the hospital. Our daughter’s RA called an ambulance for our daughter and it costs us $400 after the insurance company paid their part. Daughter is a dancer and had pulled a chest muscle. It was
NOT an emergency. We told her next time to (1) call us first if possible and (2) if it is not an emergency then take a cab to the hospital.
Wall art, tapestries (can be used as a cool curtain or to hide the items under the bed), extra pillows for propping on the bed.
Such a fun, exciting time for you and your child.