The hardest thing to do in a dorm is get a decent night's sleep. It will be even harder with 3 in the room. Someone is always coming in really late and someone else always has to be up for an early class. So you can count on having someone moving around in your room making noise and turning on lights while you are trying to get some sleep. And of course there is always a party going on across the hall. So my advice is to bring and sleep with foam ear plugs and wear a sleep mask so you can sleep through as much of that stuff as possible and maybe even stay awake in class. BTW, coffee is not a substitute for sleep in the long run.
I always had roommates that would let their alarm go off for like 5 minutes every morning. In that case, you will need a gun and at least one bullet.
Also, try to get the loft bed that is not shared. If you sleep in the bunk bed, you will feel it every time your bunk mate rolls over, etc. and it will probably wake you up. And no matter how much you like your 2 roommates, don't volunteer to remain a triple. You can still be friends from down the hall. Probably much better friends.
You will probably need to bring your own telephone and it may be handy to have an answering machine unless they have voice mail there (likely) or you will use your mobile phone to stay connected. As far as storage, just get some cheap plastic stackable crates or drawers from Walmart or Home Depot to increase your storage. For dorm living you want it to be light and cheap because you will be moving often. You may want to wait until you see your exact set-up and the space you have available to put storage containers (have a measuring tape). But you may be out of the triple within a week of moving in, so don't blow all your money setting up there. There are always a certain number of students who just don't show up for school at all for whatever reason, and they will move some students out of triples into those spaces pretty quickly.
Obviously you need your clothes, school supplies, backpack/bookbag. A student's lifestyle is very mobile and very outdoors. It will be good to have a hat, sunglasses, umbrella, a versatile jacket and shoes/boots for foul weather depending on your climate from now through mid-December. It would be nice to have something for organizing papers, such as a box to hold files (the desk may have a drawer for this). I used to rely on my bike to get around campus and around town, but most people walked. If you take your bike, don't forget a quality lock and a helmet. As for other stuff, keep it simple. If in doubt, don't bring it. You can always borrow one, get it later or have it shipped to you.
Good luck and have fun (but study first!)