We are traveling from Sevilla Sp to the Algarve coast. What is the best mode of transportation?
It would help to know where? Probably a combo of bus and train.
What do you want from 'best'? The rail networks of the two countries do not connect in the south. Any, solely, circuitous train journey to a point on the Algarve will be about 18 hours. Will you be returning to Seville? If so perhaps car rental? Bus is the other option, so, where in the Algarve?