The catch is that you will have to drag your bags up and downstairs a couple of times even though most trams have mechanic staircases. Not too bad but may be too much for older people.
The best itinerary from the airport is to take the Metro to Nuevos Ministerios, then switch to the blue line until Tribunal station and from there on take the light blue line either to Gran Via or Sol, depending where your hotel is.
The trip will take you around 45'.

