Hi and Welcome.
This post may be cut short as waiting for an bus.
Bring as little as possible to carry, have a phone with 2 sim slots so an local sim (available in airport) can give you a Portuguese phone number, have some simple "buisness" cards with your basic info so people don't have to guess your name, email address etc. and space to write your new number. With the assumptions that you are reasonably fit and able to walk a distance I'd suggest something like split your trip into a public transport part and driving part. Pick say 3 towns you may be interested in say Coimbra, Caldas da Rainha, Tomar all of which are have mainline train stations, From Lisbon airport terminal 1, straight out front door, keep going straight (1km?) then before you reach the river you'll find mainline train station and bus/coach station. having previously checked some page like Rome2rio you'll know when train departs and platform etc, also having booked some "local" accommodation at the destination on some type of AirB*B site ( I do not recommend AirB*B) as then you have contact with local plus their family and friends, ask them about everything. Spend several days walking round town, go to Tourist office, there are not many maps but tourist office should have local area, ask for where there's free WIFI as often council have set it up outside so can sip a cold beer under tree and surf, go into several LOCAL estate agents (not one of the chains) and ask for their help advice an almost any subject, generally as locals they have vast knowledge of the area and happy to talk, collect printed property details, say what you monies you may have available and ask what you get for that, or ask for rentals stuff. they will find an English speaking person. Make sure you have checked for public holidays as things do close. Most towns have an Chinese Emporium so any stuff you didn't put in your luggage should be available even if the quality is different. Take notes, notebook n pen do work well. Maybe if there are two of you then split up sometimes or you'll form (an English speaking bubble) where you obviously just speak to each other. Try to learn the pronunciation of the place names as helps to get bus tickets. Buses link most of the towns and villages but can be a bit "local". Then hop on a train to your next town, there are local trains which go to the beach, if you look on GoogleMaps then "street view" also works on some local train lines. After your towns you maybe hire a small car to check out some more rural parts, you'll have seen how people drive by then. Have a look at some site like Argus which will trawl the carhire sites to give you idea whats available, I just checked and a small automatic in February was less then 70 euro a week for us older people. Cheaper to book car online then collect rather then just go to car hire desks. Car hire need a big deposit held on credit card so often less worrying to have one own's insurance (my hire deposit cover about 40 euro a year for anywhere in EU), there's automatic tolls on motorways so an active dongle on the car screen can be added to rental and tolls taken from credit card. There's a lot of car hire places associated with the big airports so that's where they are cheapest.
My bus is arriving.
Good Luck.
PS Try and find an "History of Portugal" to read as, compared to many places the history is everywhere, also helps to understand what some people here have been through in the recent past.