I have thankfully never had an issue with my non-perishables going bad in the 11 years I've used the mini fridges at Disney. I always keep milk, butter, cream cheese, sometimes a case of water, and then leftovers and desserts from the parks. For non fridge items I get bread, bagels, cereal, apples, bananas, cheez it's, fishes, nachos and cheese sauce. I also purchase diapers and wipes. If I'm staying in a 1 bedroom villa, since i have a full kitchen I'll also purchase eggs, pasta and sauce. I like to have at least one just in case, easy, cheap, quick dinner in case something happens and we need to stay in the room for dinner (cranky kids, exhaustion, someone not feeling good, etc.). Thankfully I've never needed the pasta there but it's easy to take home if I feel like it or easy enough to leave behind as it's only $2. I only tend to get breakfast foods as I like to eat in the room before heading out as it's so, so much cheaper and I can have the kids eating while I'm getting ready.
From home I usually pack my favorite coffee, filters for the coffee pot (I bring enough to brew 2 pots a day as I bring a big thermos with me to the parks since the coffee is so gross there), and powered creamer.
My biggest advice is to try not to overshop and buy too much. I used to do that and my point of shopping to save money just went down the tubes because so much stuff wouldn't get eaten.