Medieval architecture sounds sick, those castles and old fortresses are worth the drive between cities for sure. Renting from actual owners works out cheaper and you deal with real people who give a shit about their vehicle. Each one has their own setup though, so terms vary depending on who you book with. Check where you can rent a car in Portugal here:
https://getrentacar.com/en-US/portugal . You'll find listings from private owners in different cities with their exact rates and conditions laid out. Reviews tell you if they're straight shooters or flaky, and you can message them directly to sort out details before committing.