If you are going to stay in a studio for a long period of time, especially since you are driving and don't have to worry about TSA at the airport, I would bring my things I usually have for breakfast. I'm an egg person, DH is a cereal or oatmeal type of guy. There are all kinds of "egg cooking" things at the Dollar store for use in the microwave. If you want oatmeal, bring along a large soup type mug to make instant oatmeal in. Studios have a toaster, too, so bring your English Muffins. Don't forget your butter too. If you are staying in a studio and have too much stuff for the fridge, gently place your cooler in the tub (on top of a towel so you don't scratch the tub). When you need the shower, just move the cooler into another area (again on top of a towel in case of leakage). Every studio or one bedroom I've stayed in always has a roll of paper towels in the holder and at least one under the counter; same for TP. Not sure about paper plates though....we usually stay in a studio for one night and then switch over to a one bedroom. You will be charged if you ask for MORE shampoo or coffee or dishsoap BEFORE your scheduled trash and towel day. We will always leave a note on the kitchen countertop if we need more dishwasher stuff and coffee....and another in the bathrooms for shampoo. With all of the "environmental" things Disney seems so proud of, I've discovered that if you have partially used anything....soap, laundry detergent, dish soap, dishwasher liquid, etc.....they don't seem to replenish. So....put away your half-used stuff, and leave notes for new stuff. The funny part of that is....when you bring your stuff to the trash and recycle room....there is NOT a bin for glass!!! Wait...did you not know about the trash and recycle room?
DVC rooms don't get daily room cleaning...so when your trash and recycle bins get too full and won't make it until trash and towel day, follow the signs in the hall for the trash/recycle room. When you pull out the plastic can liner, there should be a supply underneath....just pull apart your trash bag and adjust the new one over the pail.
If you run out of anything, since you have your own car, you can run out to Publix or Winn Dixie....or it you are staying at BoardWalk or BeachClub, the Speedway gas station across from BoardWalk keeps a good supply of basic foodstuffs and beer and wine. And plenty of places to eat off-site too.
Have fun! And Welcome to the DVC!