How can I determine what type of resistor, transistor and, diode I need?
Sorry to tell you this, but your circuit (as shown) won't work.

For a transistor to work as a switch (transistor dropping less than about 1/2 volt), you should design for a base current about 1/10 to 1/20 the collector current. In your case, this requires 70 to 140 mA, and there is no GPIO pin which will handle that.

So you have a choice: use a Darlington or a MOSFET. If you choose a Darlington, you can assume a gain in the vicinity of 100, for a base current around 1 to 1.5 mA. If your GPIO pin is 5 volt, this will require a base resistor of about $$R = \frac{5-1.4}{.001\text{ to }.0015} = 2.4\text{ k to } 3.6\text{ k}.$$ and allowing for the GPIO voltage being somewhat less than a nominal 5 volts suggests something like 2k.

If you use a MOSFET, you'll need to be careful about threshold voltage. If your GPIO has a 3.3 volt high level, a lot of MOSFETs are not guaranteed to turn on at this gate voltage, so you need to pay close attention to the Vgs(th) voltage, which must have a maximum value less than your minimum GPIO voltage.