sounds pretty easy.
first, you need to know what the voltage is. there are lots of ways to gather the data of when there is power.
as for the boards, the UNO with an SD card shield that has a real time clock would be the place to start.
please let us know that the thing you want to measure. as much as you can. things like motors, such as a home heater would have different places and different ways to measure.
110VAC, or any AC line, could be detected with a non-contact device such as a current transformer.
one of the problems is if say, you want to measure when a heater is on. you connect to the switch. you know when the switch is on, but if the heater is not working, you only really know when the switch is on.
we REALLY-REALLY hate to see anyone tie into mains voltages, so would prefer a non-contact method if possible.