How to choose a MOSFET
Basic things:


Supply voltage - is the MOSFET drain-source voltage rated high enough for at least 1.5x your supply voltage plus any normal expected increases?
Gate drive - not enough gate drive will ensure your MOSFET burns on heavy loads - what signal are you supplying to turn on the MOSFET?
MOSFET on-resistance and load current - how much power will be produced by the MOSFET due to its non-ideal zero-ohms on-resistance?
How quickly or how often are you switching the MOSFET on/off - losses in switching can be considerable.


When you've got all this into perspective, one of the most important graphs to look at in the data sheet is how device on-resistance varies with gate drive voltage - you may find you haven't enough gate voltage to efficiently use a MOSFET, and you might need a circuit to interface to the device.