Most of the accommodation is in Funchal but this is also where it's very touristy. For a more authentic experience, stay in a village outside of Funchal. My family and I rented a house in Caniçal, which is on the eastern side of the island, just 30 minutes from Funchal.
Recommended type of transport:
Hire a car
Using public transport:
Public transport is only fully accessible in Funchal and operates more frequently compared to other villages. However, these bus trips can take much longer to reach the destination than if you simply drove yourself there.
Hiring a car:
This is highly recommended and can be hired at the airport. We used Europcar but had to stand for 2 hours in a line to get to the counter. Every other car hire was empty (Avis, Hertz, etc) - so I'd recommend hiring from those to avoid waiting. Also, having a GPS is always useful but with all the tunnels on the island and winding roads, this sometimes doesn't work. I would recommend buying a large road map and navigating like the old days!
Restaurants & local food:
Madeiran food focuses on all things caught from the sea - one must try lapas (limpets), espada (swordfish) and polvo (octopus)! If there is a festa (local festival) taking place, be sure to go there and try espetada (barbecued beef cubes) and barbecued chicken. When in Funchal, watch out for tourist-trap restaurants: these are found along the harbour with ridiculously priced dishes. Rather buy food at a market or find restaurants away from the tourist/hotel area. On the rest of the island, you'll find that restaurants prices are cheap, and, oddly enough, the food is also better.
Water & alcohol:
You can drink from the tap in Madeira but bottled water is sold too. Drinking alcohol is acceptable at most times of day. The cheapest alcohol is Poncha, which is a traditional alcoholic drink of fruit juice mixed with aguardente spirit, honey and sugar.
The weather:
Madeira has a mild climate but the best time to visit is in summer. When I was there it was warm every day, even if overcast. Funchal is more humid, the east side is more dry and the northern side is more tropical - whereas villages at higher altitudes, like Santana, receive more rain.
Entrance fees & discounts:
Hardly any places have entrance fees. You can visit churches for free and most attractions on the island are of nature. In Funchal, a few places like Cristiano Ronaldo's museum and Blandy's wine lodge charge for tours.
Going to the beach:
All beaches are open to the public. The only time you may have to pay is if you want to use a beach chair. There are black sand beaches located at Prainha (Caniçal) & in Seixal. Other sand beaches are in Calheta & Machico. Almost every other beach consists of pebbles or stones.
Other:
It is useful to know a few Portuguese words, especially when you venture out of Funchal into more rural areas. Locals in these outside villages are generally friendly so you won't have a problem if you can't fully understand.