Brake and derailleur adjustments:
I adjust the rear brake first because I use it to stop the rear wheel while I'm making rear derailleur adjustments.
I adjust the rear derailleur before the front because I shift from the little to the big cog when I'm adjusting the front derailleur.
Immediately after I finish adjusting either a brake or a derailleur, I trim the cable. That way, if I get distracted, I'll have a reminder of where I left off.