AC power supply safety
Anything touching the power transformer primary side (line cord, connectors, switches, fuses, etc.; and of course the transformer itself) should be UL listed.  Any conductive surface that might come in contact with the user must be double-insulated.  There are spacing rules regarding how close together conductors can be, and there are similar rules for the high voltage secondary circuits.  If the final assembly is in an insulated box, that is the majority of the protection for the user.

UL1950 / 60950 / EN60950 is the standard covering personal computers, and is a good standard for general use.  Medical devices have a more restrictive standard.

Shielding is a different matter, and gets into FCC part 15 rules.  But for a linear amplifier with a linear power supply, the major shielding issue concerns keeping noise out of the circuits, not preventing the circuits from interfering with other devices.