We went to Portugal in March. A great trip.
We flew into Lisbon and took a taxi to our hotel in the heart of Avenida de Liberdade, which was a really worthwhile location because we could walk to a lot of the downtown area highlights all the way down to the shore. Also took a tuk tuk tour around other parts of Lisbon - the old town and Belem, which was a lot of fun with a local guide. We reserved that through the hotel with a company they liked, rather than grab a random one along the curb, which sometimes aren't licensed and they told us could be subject to being stopped by the police and halted. Not sure how often that happens, but didn't want to chance it.
Then we took a cab to the airport where we picked up a car to go to Porto and then the Algarve. You should get the Via Verda toll transponder activated too for highway use.
Glad that we didn't try to drive within Lisbon, not so straightforward. Even getting out of the airport with the rental car, we got stuck on a 6-8 lane roundabout with 2 traffic signals for different directions leaving the roundabout. Very confusing and I ran a red arrow accidentally and got honked at. Driving was fine and easy on the highways and smaller cities, but definitely need a navigation device either on your cell phone or in the car once you get into the urban areas.
We stayed in Sintra with the car. Was a bit tricky getting to the hotel in the heart of town with narrow roads and alleys, but the nav device got us there. If you take transit there from Lisbon, maybe want to start early. It's worth seeing multiple castles there, and once in town, there are good bus and other options for getting to them. A few of the castles have nice forest trails to walk in also, with ponds and various structures along the way. Adds time to the trip, and also you need reservations if you want to get into the Pena castle especially.