One of the big draws to Challaborough is the rural location; you really are in the middle of nowhere. This is what makes the place so special, but can feel frustratingly inconvenient. There actually are a good range of shops nearby that will fulfil all your needs.
It's good to buy locally and you won't pay much more for the privilege here, your choice will not be limited. There is a convenience store in Challaborough itself, which is very well stocked. They have a good range of basics and more, but you might struggle to feed your family for more than a day or two from here. Newspapers, booze, confectionary, beach goods, suncream all in abundance; but you will need to go a little further afield to really stock up.
There is an excellent farm food shop located at the top of the lane that snakes up the Eastern side of the valley. It's about a 5 min drive or 30 min walk depending on which way you go. Depending on the seasons they have a wide range of fresh, locally grow fruit and veg.
Up the Eastern cliff path you come to Bigbury-on-Sea. If you are after wetsuits and beach wear, there is a good shop located down at the main car park.
Slightly further afield (and you will need to drive), there is a larger mini market and Post Office at St Anne's Chapel. There is ample parking at the rear of the shop, and again you will be amazed how well stocked this store is. They have fresh meat, veg and a wide selection of other produce.
Another 10 minutes drive beyond St Anne's Chapel there is Modbury, which has a coop at the bottom of the high street. Modbury is 'famous' for being the first town to ban plastic carrier bags, so you will need to bring you own.
The closest large Supermarket is probably Kingsbridge. There is a Morrisons and a Tesco's. Ivybridge also has a large Tesco store, and there is a large Morrisons in Plymstock.