Short answer
There is no single best island: it depends on whether you need jobs, schools, healthcare and an airport, or prefer quiet and lower costs. São Miguel and Terceira offer the most services and work opportunities, while smaller islands like Flores, Corvo or Graciosa suit people seeking calm and nature. Visit in different seasons and check healthcare, transport and internet before deciding.
General information, not legal or tax advice. Rules and amounts change: confirm with official sources.