If you are a meat lover and would like to try Madeira's signature dish "Espetada" (beef on a spit) then these are my favourite on the island;
Restaurante O Viola is our first go-to recommendations for authentic cooking and excellent value. Start your meal with their delicious Piri Piri Quail starters to share followed by Espetada - be sure to ask for the bay leaf skewer which imparts its flavours to the meat (note, if you like your meat 'cooked through', maybe go with the metal skewer instead, as the wood in the bay leaf will leave the inside a rarer), and order side dishes such as the salad, fries and the other Madeiran speciality, Milho Frito (deep-fried polenta cubes).
There's a great wine list but with Espetada, I prefer reds from the Alentejo region (south of Lisbon), usually soft, rich, intense and full bodied.
This restaurant is very much of a favourite of local families with a relaxed ambience, and there is a good chance you will be the only tourists in there. Busy times can be busy; dress casual and comfortable. They also have a good size car park around the back - driving there is kind of essential as it is about half an hour from Funchal.
Restaurante Santo Antonio is yet another go-to favourite of our for a similar experience located in the same Parish, just a little further up the hill.
They also have a car park if you are driving but it is very steep.
Restaurant O Lagar is another restaurant in the area for similar local cuisine, particularly Espetada. It is a nice mixture of local families and tourists but there are occasional coach parties, as they provide entertainment, including local folk-dancing (Bailinho - which you might be encouraged to join in!).