This was my list for DS last year. His dorm room included a combo microwave/fridge/freezer, so we didn't have to get that.
Power strip
desk lamp
over-the-door hooks (great for towels and coats)
dry erase board (although DS didn't end up using it)
set of plastic drawers (the three-drawer kind -- holds anything, great to put
the printer on top of it)
small first aid kit
shower tote
paper plates, bowls, paper towels, plastic silverware
office supplies -- scissors, stapler, paper clips, butterfly clips, ruler, scotch tape,
duct tape, etc.
large and #10 envelopes, couple of stamps
small tool kit -- screwdriver, little hammer, flashlight
fan
small sewing kit
calendar
computer, printer, paper (even if there's a central printer, this is useful)
school supplies -- folders, spiral notebooks, sharpie, pens, pencils
bedding, including a throw, and a 2" thick foam pad for under the mattress pad
two sets of towels
area rug
back rest pillow
laundry basket or collapsible hamper
wastebasket (our school said no plastic wastebaskets -- not quite sure why), with
small trash can liners (much easier to get rid of the garbage and not have the
basket smell bad)
kleenex
Clorox cloths, several of various size ziploc bags, a small box of large garbage bags
(these were handy for all kinds of things, including protecting kids and books
in the rain)
Purex 3-in-1 laundry sheets -- MUCH more convenient than lugging detergent and
softener
closet organizer of some kind -- he had both a hanging shelf (from the
closet rod) and a put together three-shelf thing that sat on the floor (my DS
is a clothes horse)
Basic dorm food -- soda, poptarts, Kraft easymac, granola bars, favorite snacks
We ended up swapping out the desk chair they provided with our own chair (and switched back when he came home). His roommate lofted his bed and brought a wing chair. If there's room and the roommates want one, you could get one of those small couch/futons that they have at Target to put under a lofted bed.
Our DS did not have a TV, or use an umbrella. He is going to a different school this fall, and now thinks he wants a TV, but he will be in an apartment-style dorm (two 2-guy bedrooms, full kitchen and living room) and doesn't know yet what's included.
I wouldn't wait until you get your child to school unless you're travelling a long distance and don't want to bring stuff with you. Some stuff you can get on campus, but your child will most likely be itching for you to leave so they can get on with starting college life, and won't want to take a trip to Target or
WalMart. And at that point, you might not be able to get decent prices on some things.