You still have not stated clearly which areas of Portugal you wish to visit from Spain!
In all, I would say that Madrid is the best jumping off point to visit Portugal as there are low cost flights from Madrid to Lisbon and Porto. There are also good regular bus services between Madrid and Lisbon.
There are no direct connections between Gibratar and Portugal. It is possible, however, to get a buses from Algeciras to Seville and then connect to a twice-daily bus to Faro and Lagos in the Algarve Region of Portugal or to the daily bus from Seville to Lisbon.
