I will be away for 3 weeks in December and plan to shut off my water supply and put my water heater on vacation setting. Is this the right thing to do? Also, I have a recirculating pump, do I need to turn it off as well?

Depends on where you live. If you live where it will go below freezing it is a bad idea. Just turn temp down to lowest until you return if this is the case. DrTom4444