If I have a microcontroller circuit mounted inside a metal enclosure powered off a 12V DC PSU, is it good practice or recommended to connect the PCB ground to the enclosure?

 

Connect the ground wire from the AC connection, I wouldn't bother with the ground from the 5V circuit. Since the idea of connecting a ground to the chassis is to reduce shocks from high voltage wiring, then there is no need to connect a ground from 5V circuits. There also might be feedback that can cause strange behaviour.