Blue Line & Shuttle, definitely. If going to C or E, you also save trip time much of the day versus the Silver Line starting at A and working around.
Really the only annoyance now with the Massport shuttles is the excessive wait time inbound to the terminals at the rental car facility. At least when departing the terminals the buses go straight to drop off at the Blue Line.
For the State St connection, going to the Blue Line en route to the airport, sitting at the rear of the southbound Orange Line train will cut down on the long transfer walk. Going the other way (back to Wellington) fortunately the connecting passage is much shorter!