I am thinking outside Lisbon in the hope I can save some costs on accommodation
You really need to clarify costs as they are highly subjective to different people.
We are in Lisbon just south of the airport. We live between the Alameda and Arroios metro stops. When we fly out of the Lisbon airport, we walk 5-10 minutes to the Alameda metro, and it takes us roughly 20 minutes on the metro before we are at the airport. Total cost for the two of us on the metro now is I think roughly €3 per journey. When we use Oriente for the bus or train it is a few stops before the airport so roughly a total of 20 minutes.
As @thomasribatejo stated we need to plan our airport, bus, and train times around the metro schedule or just use a rideshare like Bolt.
Our furnished T2 is €1,400 a month. We have no transportation costs unless we are feeling lazy and grab the metro so that costs us less than €20 a month for the two of us. Having everything we need within a short walk or quick metro ride has some value to us after being stuck in a remote town in the US during Covid.