An inverter wastes a lot of energy, plus it's not needed.
I have no mains power in the barn, and necessity being "the mother of invention", here's my setup:
12V 7W solar panel, charge controller, 12V deep cycle battery (I'm using a car jumper box), digital programmable 12v timer/switch ($7.99 on Ebay), 12V LED light (I'm using 2W, might upgrade to 3-5W).
I also have the pop door on a programmable timer run 3 way double-pole, double-throw switch that runs a car window motor to turn a pulley with a cable on it. Switch at the top to shut it off when it opens, switch at the bottom to shut it off when it closes.
Much more efficient than changing 12V DC to 110V AC, which means you can use a smaller panel and battery.