Appropriate base resistor for BJT switch driving a motor
A MOSFET if really best for turning on high current loads, esp motors that, as part of their nature, have a very heavy start current that you do not want to accidentally limit. 

Using a BJT means whatever is driving this circuit does, in turn, need to supply enough current to drive the base, so you end up passing the problem backwards. A MOSFET, being voltage activated, is much more suitable to be controlled by logic circuits.

Choose a MOSFET that has:


Enough current capability to handle the full start-up motor current indefinitely.
A Vgs threshold no more than 1/3rd of your logic output level and make the gate resistor small... ~50R.
An RDS_ON value that is very small. They come in all shapes and sizes, and the lower the RDS_ON the less power and heat will be wasted/dissipated in the MOSFET.
Is in the right package to not be overly hot when running, or can be attached easily to a heat-sink. (Do the math to figure out if you need one, and add it, BEFORE you power it up.)