Cobble Corner: the Post Office and small convenience store in Marazion. Good for emergency bread, eggs and butter and they do stock beer and wine.
Drive out toward Penznace and the first place you will come to is Long Rock. Here you will find all the major supermarkets, some with petrol stations and some useful large stores: Sainsburys, Morrisons, Lidl, Tesco, The Range, Dixons, B&M.