If you are trying to explore all three areas in a week, you are wasting your time. You will spend a great deal of time in just transportation. It is 3.5 hours from Porto to Lisbon, and then another 4.5 hours to the Algarve area. And an average of 2 days in each area won´t give you a good feel of the locality. At best you will get the tourist feel, but have no idea if it would be a place to live. I would suggest digitally exploring areas first (Youtube, Rick Steves, online travel books, etc especially from an expat point of view). Already have a budget in mind before you look. In 2018, ours was $3000 per month and we already knew that we couldn´t afford the Lisbon and the Algarve areas, so why waste time exploring there, especially when we could visit later? Have other factors already decided too, like weather as both the Algarve and Lisbon areas are much warmer than the north. Walkability. Algarve area is mostly small towns and villages and can be difficult to get around without a car. Lisbon has wonderful mass transportation, but is spread out and very hilly. Porto is smaller, and good transportation but also very hilly. Braga is very walkable and mostly flat, but the international airport is a 45 minute bus ride away.
Before our exploratory visit in 2016, we had already decided a northern Portugal or southern Spain. We planned on a week in northern Portugal and 4 days in southern Spain. After three days in Braga, we knew we had found our new home and spent the rest of the time actually learning the city and then just touring Spain a little. But we had basically already settled on two places before we even arrived through our research. I suggest that you do the same.