As others have said Silver is particularly handy in your case: fast track, increased baggage allowance, free seat selection, double Avios and lounge access are stunning when your flights are in WT/WTP.
To keep costs down you might book your flights during a sale, staring from a European city can make you save lots of money and earn more TPs and Avios.
A mini TPs run is perfectly doable when you're in the US, spending little both in terms of money and time.
Washington is receiving the A380 in October as well as a new lounge, silver is for sure useful to maximize your trips.