Transportation
This dependence highly on what you want to do. It is easy to rent a car at the airport and go around on your own for a road trip. Madeira is a small island, it can be surrounded with a car in ~3 hours.
When it comes to hiking in Madeira transportation get a bit tricky because the most of the longer hikes are point-to-point hikes. Which means you would need transport to the beginning and a pickup at the end of the hike. With that in mind there are 3 options in place: take a cab, take the bus or find a travel agency that books together the hikes you want to do with the transport included.