There are 3 supermarkets on Achill Island. The largest one is probably Sweeny's Supervalu in Achill Sound (Half the Island seems to belong to the Sweeney and Lavelle families :-). There also is another supermarket in Achill Sound. The island's 3rd supermarket is located in Keel. It's slightly smaller and more expensive than the Achill Sound Supervalu, but for the Keel residents, it will do in most cases. Cash machine and post offices on the premises. Keel has a very good butcher shop, Calvey's, who also supplies many of the island's restaurants. We bought steaks and chicken breasts there -- both were of very good quality.
The nearest "real" supermarkets are in Castlebar which is 50 km away. If you come by car and are doing self catering on Achill, try to bring some basic food from home and/or stock up some stuff en route in Sligo, Castlebar or Galway.
If you don't want to cook yourself but live on a budget, Keel does have a fish & chip takeaway, the food is okay and reasonably priced. The Graceland chinese restaurant also has a moderately priced take away menu -- probably the best value for money on the island.
What to buy: Achill Island has a couple of galleries and craft shops, most of them being located in Keel and Achill Sound
What to pay: more than average, for German tourists Ireland and particularly Achill is an expensive place. We were told however that nearly everywhere, you get value for money and from my experiences I would support this statement.
The Beehive is a well-stocked craft shop and cafe. It makes a nice place to have lunch or beat the clock when it's raining outside. Don't buy a CD there, though, the selection is limited and the prices are ridiculous!
Despite the loose gravel and the steep ramp, wheelchair access inside is very good.
What to buy: Local maps and guides, greeting cards, gifts, crafts, pottery, silverware
What to pay: slightly more than average