The most efficient switch is mechanical but the life of a mechanical switch is not long, so the next best thing is a transistor. Depending on the frequency of switching, a bipolar transistor can be very efficient, altho mosfets are popular nowdays. At high frequency, it takes a lot of power to drive the input capacitance of a mosfet, so a bipolar might be a good tradeoff in some cases. Power loss in the transistor is due to the finite switching time and the voltage drop when "on". To minimize I squared R losses, make the main battery voltage as high as possible.
When voltage is applied to the coil, the current increases exponentially, eventually reaching the point where the iron in the core saturates. The coil then looks like a short circuit and produces smoke and fire, so you don't want to go that far. The energy stored in the coil (inductor) is 1/2L*I^2, so you have to compromise between I^2*R losses and I^2*L storage.
For long term output storage, use a battery. Or, for short term storage, a capacitor with high peak current and low resistance ratings will work. Or, use both, because the battery probably has high resistance to high peak currents.