Seven days is the sweet spot — enough to do two full-day hikes, the Pico do Arieiro sunrise, a north-coast loop, Porto Santo as a day trip, plus Funchal time. Five days works if you skip Porto Santo. Three days is enough to see Funchal, one viewpoint and one short levada — but you'll want to come back.
A typical first-time itinerary that holds together: day 1 Funchal old town, day 2 levada walk (Caldeirão Verde or Levada do Rei), day 3 east tip (Ponta de São Lourenço + Machico), day 4 Pico do Arieiro sunrise + south-coast pool afternoon, day 5 north-coast loop (Santana, São Vicente, Porto Moniz), day 6 west coast (Calheta, Paúl da Serra, Fanal), day 7 buffer / Porto Santo day trip.
Madeira distances look short on a map but mountain roads slow everything down — assume 30 km/h average outside the expressways.
Many visitors who stay 10+ days end up returning to favourite spots rather than discovering new ones — the island is small enough that a week covers the headline sights.