The nearest supermarket is the one by the Triangulo Restaurant. The Intermarché supermarket is about 2km away depending where you are staying In Porto de Mós.
To get into Lagos, you will not route via the coast. The roads in the area and into town are all tarred, with pavements and good lighting. Be aware that the walk back up from Lagos can be a bit of a haul.
There is a cliff-top path running from Porto de Mós beach to the cliffs overlooking Praia da Luz. Be careful if using it, as parts of the cliff are eroding.
There is a steep path down the cliff to Praia da Luz. One will need to be fit.