Should I unplug the timer on the water heater when shutting off water to the house?
I wouldn't bother unless you're going to have your water turned off for a couple days.  In that case, turn off the water heater itself.  You'll have a hard time using any hot water with the main turned off, so it is mainly a consideration of whether or not it's worth it to keep the water in the tank hot over the period you won't be using it.