There are just so many to choose from.I use the BD679 darlington driver but there are lots more.However a FET will dissipate less heat on heavy loads so look at a IRLB8748 or other similar logic level FET.Normally people use stepping motors for a CNC.
As Mike says, a logic-level MOSFET would be better, it will run cooler and have less voltage drop. Also if you get an avalanche-rated one it is reasonably tolerant of back emf when switching inductive loads like motors. I use type STP40NF10L. At 100V 40A it's overkill for your application but will work just fine.
For a 12V 1A motor, wouldn't a simple TIP120 be fine? Are they not fast enough for PWM or something?
For a FET there is no need for a resistor as such because the gate is high impedance so you can do without. However if it is being switched very fast with PWM then you are best with a series 100R to limit the current out of the arduino to safe levels. This is because a gate looks like a discharged capacitor and that initially is a short circuit.
If its N-channel, I'd add 10K pulldown resister to ground on the gate as well so the MOSFET won't be on as the arduino starts up and the pins are inputs before the sketch starts and drives the pin low.Or a pullup if you want it on to start.
They are inputs when powered up or Reset. State will be unknown.10K will pull them low.Use 5K, 1K, anything down to ~220 ohms.
I am in the UK so I got my STP40NF10L mosfets from www.rapidonline.com, however you can also get them from Farnell/Newark and Digikey.I also recommend a pulldown resistor with mosfets (I use 100K), and the 100 ohm series resistor suggested by Mike if you are doing PWM.
I am doubtful of the assertion that the 12V motor will take less than 1A... Unless its a unipolar stepper motor I suspect the winding resistance is low enough to pull many amps stall current. The current a motor takes at no load when up to speed is a tiny fraction of the stall current.
Move the NPN/N-channel transistor so it goes between the motor and Ground.NPN/N-channel are better as a current "sink" than as a current "source".With the NPN also put a 150 ohm resistor between the arduino pin and the base so you don't overcurrent the output pin.