But what order should I adjust things in? Is there a typical way to adjust a DMMs or is it manufacturer/product dependent?
Every dmm uses a internal dc reference voltage to reference the measured voltage against.
If you find that dc volts/amps and ac volts/amps are all reading the same percentage offf then this reference voltage could be the likely cause and needs readjusting also a dirty trimmer is not uncommon in these type of dmm's
If only ac volts/amps are off then the gain for the ac amplifier has drifted and needs adjusting.
The ohms ranges typically use fixed value reference resistors but on some meters there are also trimmers added to those.
Take a look as to what dmm chip is used in your dmm (probably some intersil icl Type) the datasheet of it should contain much useful documentation.
Or look for the schematic of a dmm that uses the same chip (keithley, fluke) from that same era.