Factors to decide:
* whether to use mosfets or transistors. Transistors are robust and not as easily damaged by high voltage spikes (which are likely from a 2A motor).
* whether to use N or P devices for high-side switching. A P-device has its bias referenced to the positive supply, making it easier to turn on.
An N-device will need more than 12V to turn it on at the high side.
* For low-side switching, if it were me building it I would reach in my junk box for 2N3055 (TO-3 package). It will easily handle 2 Amperes at 12V. I use 2N3055 in my homemade power supply which provides up to 3.5A due to heat-sinking to the steel housing.