Fire away.
Typical.
How about a simple NPN transistor? power MOSFETs generally require a gate voltage that exceeds the drain, which will be at 12V.
You can use an NPN power transistor as long as the current requirements of your device doesn't exceed the current the micro I/O pin can supply. The hfe for a 2N3055 ranges from 20 to 70 for example. So an I/O pin that can supply 20ma to the base and control a load between 400ma and 1.4A.
You could use a darlington arrangement if you need to drive a larger load.
Finally if you used a relay, you would still need a transistor relay driver to drive the relay.
How much?
Now a relay could be useful here because you could run the circuit through the normally closed contacts. No power would be consumed the majority of the time. Activating the relay would turn the device off.
BAJ