Everyone has his favorite, talking about levadawalks and explorings at Madeira. I have walked some of them through more than 13 years. Here is two of my favorites - totally different from each other, but both with a spesific beauty you will remember for ever. Both my favorites you can walk without guid, with good shoes and a bottle with water. BUT: Take care, take time, take the silence.
For the preparence. Buy the book: Madeira car tours and walks, of: John & Pat Underwood. My reference is according to this book.