Is this MOSFET a good choice? PWM -> FET -> DC Fan
That is not a suitable transistor for this application since you want to drive the base with 3.3V.  The 60V rating is also overkill.

A much better fit for this application is the IRLML2502.  That is specified for lower gate voltage.  It can only handle 20V, but that's well above your 12V spec.

The body diode is not in the right place to serve as a load flyback diode.  Think of the load as a inductor, and you'll see that it will try to make a high voltage when turned off, not a low voltage.  You still need a reverse diode accross the load (the fan in this case).  Make sure the diode is rated for at least the same current as the fan.  A regular silicon diode will be fine as long as you turn the fan only on or off, and don't try to turn it on shortly after having turned it off.  If you plan to do PWM control, then use a Schottky diode since those have essentially zero reverse recovery time for this purpose.  It will also be slightly more efficient.  At 12V it will be no problem finding a suitable Schottky diode.