Zapping, using an electronic card is probably the best inter-modal transport payment system for Lisbon. Once you’ve bought the card (50c) and loaded it with credit, you can use it to pay-as-you-go on buses, the metro, trams, trains and ferries.
The Lisbon card is also useful but how early you start using it will depend on what you want to do with it e.g. visiting Belem or Sintra, museums and galleries, travelling around Lisbon? It might be worth getting the 72 hours Lisboa Card from the Information Centre in Lisbon city when you’ve found your feet.
In Carcavelos, you’ll be just 20mins by (frequent) train to Lisbon’s city centre and 10 minutes to Cascais.
Do you plan to hire a car to travel around in? In addition to airport based car rental services there’s a non-airport based service in Cascais. And if you can find a space, there is free car parking in front of the apartment. Outside the square, parking must be paid for.