How do I choose what type of transistor to use?
Silly to entertain using a BJT for this. You want to use a P-channel MOSFET. You can turn it on with another (small) N-channel mosfet such as a BSS138. See below.
It is true that the control signal to the servo may need to be low at all times when the PMOS is switched off. I haven't played with servos enough to be sure about that. You may need to write your code so that after you turn on the PMOS, wait 50ms or something before you start controlling the servo. And stop controlling the servo before you turn off the PMOS. By &quot;stop controlling the servo&quot; I mean force the control signal to be low continuously.



simulate this circuit &ndash; Schematic created using CircuitLab