Welcome to flyertalk yxu1215.
Greece has two airline brands operating under one company. Olympic Air and Aegean. Aegean is a Star Alliance member. Olympic and Aegean are the only carriers that have regular service to all the Greek islands. In addition mostly European charter airlines offer flights from Europe to the Greek Islands. Regular European airlines (like Lufthansa, Air France, KLM, British Airways, etc.) offer mostly only flights to Athens and Thessaloniki. So first choice for you would be United because of the Star Alliance membership of United and Aegean.