Hi Bruce, Welcome to the DIS.
I'm certain there is a store at the cabins that you'll be able to buy what you need, but I would expect it is quite a bit more expensive than the local supermarkets, if the other WDW outlets are a decent guide.
I have found Publix to be the best mix of value and quality. You will find that Walmart ( along the 192) is probably cheaper and the Goodings ( at Crossroads) is arguably better quality ( but a lot more expensive).
The nearest Publix to WDW is found by going to the Crossroads area to Apopka Vinelane Road ( I think it's state road 525) and heading (South) towards the 192. This road comes to a T junction with the 192 and the Publix is on the left hand side of that junction. You may have to do a Uturn or there may be an access road just before you get to the lights , I can't remember fully.