Shopping for food
There are a number of alternatives to buy food:

There is a (very) small supermarket in Les Masses (close to the chalet) and one in Les Collons. These have very limited ranges and are probably best for emergency top ups!
There is a larger (but still not large) supermarket in Heremence, as well as a boulangerie and boucherie. The supermarket has a reasonable range (particularly given the size) so you may want to use it if you need a few things during the week. It is on the road behind the tourist office (a sharp right had turn if you are coming from the chalet). There are similar amenities in Vex.

The main supermarkets are either in Sion (Migros, Co-op and Aldi) or Conthey (Migros, Co-op, Lidl) which is just off junction 25 of route 9. The stores in Conthey are probably larger, and I find it just as quick to get to – the best is probably the Co-op: just take the Conthey exit and follow the road until you reach the shops. There is also a large assortment of non-food shops.

There are some lovely specialist food shops in the old centre of Sion – well worth a visit, but probably not enough for a full shop.
You will need to take bags to carry your food in (they are not supplied) or to buy them at the supermarket. There is a supply of reusable bags in the utility room for you to use while you are here. Most supermarkets are closed on Sunday but the mini supermarkets in Heremence and Vex are open on Sunday mornings.

Other shopping
There is a broad range of chain stores including C&A, H&M, Conforama, Jumbo, sports shops, etc. in the shopping centre at Conthey.

The Old Town in Sion has a more interesting selection of specialist stores. Start at Rue du Grand-Pont and explore the surrounding streets.