We went in Sept. and took 2 large suitcases, 1 small, kids each carried on backpacks (I won't do that next time because they didn't use anything in them). I carried on my camera and diaper bag. Next time, we will probably take 1 more smaller suitcase. Remember if you have the really large suitcase, if you go over a certain weight (maybe 50 lb) you will have to pay extra for the baggage.
I looked at your signature, it shows you're doing a split stay, with the 2nd being BWV. Remember that if you're in a studio, you will have access to a washer & dryer and if you're in a 1 bedroom or larger you will have washer & dryer in your room. I love this because we can pack much less and just wash a few loads of clothes while down there.
Also, you mentioned packing food, have you considered using a grocery delivery service such as wegoshop.com or gardengrocer.com? We've used wegoshop twice with no problems.
We are a family of 5, next year we are going to try to eliminate carry ons with the exception of a diaper bag & my camera bag. We will check our stroller and just let DD ride in her carseat (we bought a little carseat carrier on wheels that she can ride in). The more carryons you have the bigger the pain getting through security, taking shoes off, there just seemed to be so much stuff. I felt like we were clogging up the area.
Have a great trip!!!