I had been looking at using a deep draw battery. I don't have a block heater so would try and get a 12v one, if they are available, so I would not need the inverter.
The garage itself is fairly well insulated in that the door is the only outside surface and that faces away from the prevailing wind. The roof is a heavy concrete plinth, with a heated house on top of it.
This is a picture of my old car outside the garage, to give you an idea of the set up. I now have a new door without windows in it!