Senior at college, here!
My freshman year I lived in a small dorm on campus with a friend I'd known since elementary school (such a mistake). The room was tiny. Most dorm beds are Twin XL, so go for that type of bedding. I would also recommend a mattress pad. I never got one and the bed was super hard...I got used to it after a while, but had my parents bought me a nice one I would've been very thankful (my roommate had one and her bed was MUCH softer because of it).
Our dorm didn't come with a fridge, so we got one of those (we did have a communal fridge for our whole hall, but I didn't use it because I didn't want anyone taking my stuff). We also had a microwave + microwavable bowls, plates, etc. We just had plastic silverware to throw away when we were done in order to keep the amount of stuff to wash down (especially since my roommate refused to wash her dishes she made

). I think my roommate also had a coffee pot, but since I lived on campus I would just use my food dollars (most universities have something similar--parents can upload cash to the students account and they have money for food on campus) for Dunkin Donuts or Starbucks (however, when I moved off campus my sophomore year, I got a Kuerig and have used it soooo much ever since).
Our room came with ethernet cords plus a desk for each of us, so really just a bit of organization accessories for the desk are helpful. Something to keep pens and pencils in, some sort of paper/file organizer. Just the basics.
My roommate brought a small tv that she got before college. It was basically one of those cheap $100 tv's from
Best Buy that are like 19". It worked for the room since it was so small, though if you are looking for a gift that you want them to keep for a while, I'd recommend investing in something a bit larger (to put it into perspective, I got a $100 tv for my apartment my sophomore year, but later upgraded to a $300 tv my junior year...it would've just been more cost effective to start off with the $300 tv, because the small one is just sitting in storage...) Granted, this depends on the size of the dorm room.
Personally, I also took the majority of my books and movies from home because I like to have them. For those I needed a bookshelf. It was small and just three shelves worth, but it fit the books and movies that I really wanted at school. We just put the tv on top of the shelf (again, depends on the shelf and size of the tv...) so we didn't buy any sort of stand for the tv.
My dorm room was on a hall, so bathroom supplies were there for us (well, usually) so we didn't have to buy toilet paper or cleaning supplies. We did, however, use shower shoes because well...common sense, and we needed a small shower tote to take our shampoo, conditioner, soap, etc. I just used a super small one because that's basically all I took and I just changed once I got to my room (some people would change in the shower and thus brought more bags to carry their clothes, kind of depends on the person and how comfortable they are with their roommate).
I think that's about all I used! I didn't buy any storage containers, nor did my roommate. She had one but it didn't move for the whole year and was just filled with clothes she didn't wear.
Obviously things like hangers, maybe some extra underwear and socks, and toiletries were the best gifts. Candles aren't permitted unfortunately, but I used one of the wallflower plug ins and no one ever complained, but you might want to check with the university.
Sorry that's a novel, but if you have any questions, feel free to ask!