Transistor Switch for my Raspberry Pi 3 FAN
Try using a common switching transistor such as 2N4401. You should have Ib in the range of the fan current divided by 20 to have the transistor fairly well saturated. 10:1 (Ic/Ib) would conform to the guaranteed specs, but 20:1 is good enough for this, at 200mA or less. If you look at Fig 17 in the linked datasheet, things go pear shaped at higher collector currents: 



If you had a much higher current fan, it would likely be better to use a MOSFET rather than a BJT. 

@Dampaskin's suggestion of 220 ohms for the base resistor will be fine for this. And you're done.