There is a small local supermarket which sells most everyday goods including fresh bread, greengrocery, good ham, cheese, beer and wine about 5 minutes walk down the hill at El Coto.
There is an excellent bakery for bread, cakes and empanada (a kind of light pie usually with tuna and tomato filling).
There is also a pharmacy, hairdresser and takeaway pizzeria.
The best supermarket is Carrefour, first right at the third roundabout 1.5 km down the hill. You will probably be able to get everything you need here at good prices. It is open normally until 10 pm Mon - Sat, but is often closed on Sundays as are most other shops, except July and August
There is also Mercadona on the left before Carrefour; generally less choice but possibly better prices. Both have very impressive fish counters. You should be able to find all your needs here.
Supposedly the largest Corte Ingles (large up-market department store) in Spain is within walking distance (go down the hill to the second roundabout and follow the signs). This also has a large supermarket (Hipercor) which is very good, though more expensive than the others..
There is another Carrfour hypermarket and large shopping mall three exits along the A7 towards Marbella. This is claimed to be the biggest complex in southern Spain and contains around 30 shops and a number of screens in the multiplex centre, as well as restaurants.
There are two Lidl stores, one just beyond the Corte Ingles, the other near Dunnes. There is a mini-mall near Dunnes (go to the Coin turn-off, and take the second exit from the roundabout) with various shops including Lidl. Finally there is an Aldi on the Coin road.
Further afield, there is a Carrefour near Malaga (just after the airport turnoff) and an Al Campo at La Canada shopping complex at K182 (just before Marbella) both of which are somewhat larger than the Euromarket.
In the centre of Fuengirola there are a large number of fashion and shoe shops, and there is an indoor bazaar selling leather wear, clothes, shoes, souvenirs etc. There is also a very good indoor market (at the bottom of Carretera de Mijas) selling good meat, fish and greengrocery.
Mijas has all you could want in the “touristy” line, but some very good quality leather jackets and other products.
On Sunday mornings there is a market at the western end of Fuengirola one block back from the beach, selling mainly clothes and pottery. (In the summer months, this becomes a night market).
There is a market on the fairground (Recinta ferial) on Tuesdays and Saturdays. This has furniture, bootleg CD’s, etc. However this sometimes disappears if there is a feria, in which case all the small societies have an open house with food, wine and beer.
There are other similar markets at La Cala (Tuesdays and Saturdays) and Arroya de Miel (Fridays and Sundays).