Calculating base current and resistor required from transistor datasheet? Do I need a different transistor?
Well thought out and written question.  

You are quite correct in your calculations, the 4V Vce is important, it means you need a 16V supply or else your motor will only see 8V and run slow and under power.  This lost power will heat up the transistor at 4V x 1.5A = 6W so require a heat sink.  The current will likely be a bit lower as the motor is getting less than 12V but not neat 480mA

To get the full current even with the 16V supply the low hfe means that you need to find more gain and this is usually done with a logic buffer to give you the extra drive or an extra transistor to amplify the logic output.

As others have suggested a logic drive MOSFET is a strong contender as long as you are not trying to switch it at high speeds to control the motor speed, this will cause heating in the MOSFET if you do not make use of more elaborate gate drive control.

While starting out in an effort to minimise the risk of having motor voltage reach your controller (and for general galvanic isolation for a lot of reasons) I would recommend a relay as well. The relay you can usually drive with a single transistor and it would be selected to drive the motor with a safe margin. 

Remember that your motor starting current may be much higher than the rated running current and if your transistor or relay contact are rated too low you may have regular failures.  A 5A rating would be a happy margin.

As mentioned you want a fly-back or free-wheeling diode across the motor (or relay) coil to protect your transistor.

EDIT:
There are also darlington transistors available and these can be used but will have the same high Vce saturation voltage. Your load of 12V and 1.5A is often these days handled with MOSFET or relay when using microcontrollers.

Here is a picture search that may help find ideas.  There are lots of alternatives that are worth considering to find what will suit you best.

https://www.google.com/search?q=motor%20+drive+transistor+arduino+schematic+12v+2a+-stepper&amp;tbm=isch