To get the most of your journey, on leaving Lisbon you should travel by car. The roads are excellent, and with GPS guidance you will have no problem finding your way (I used to do it with paper maps, using small country roads to see the villages and find hidden treasures). Driving gives you the freedom to travel at your own pace, stop in unexpected places, find typical restaurants along the way, and in general get a much more full experience Portugal and its friendly, welcoming people.