My DW and I spent two weeks in an independent vacation of Portugal. We visited Lisbon, Obidos, Coimbra, and the Evora (Spanish border) area before coming south to the Algarve. We stayed for three days in Sagres, had a wonderful time. Issues:
1. We traveled in mid September, weather was warm and sunny, the water off of Sagres was warmish, good for swimming. Note, March will be spring weather, the water will be too cold to swim in.
2. Albufiera is a big Brit vacation and retirement community, and fairly heavily developed.
3. Take some tours, there's lots of history and breath taking scenery. In Sagres you can see Henry the Navigators fort. Going the other direction (East) you can go as far as Cadiz in Spain.
4. Food and wine were wonderful all over Portugal.
5. See a Fado performance - soulfull Prtuguese music.
6. Learn some basic Portuguese phrases - You'll get better reactions from the natives.
Have a wonderful time!