For batteries, I have several "loose", two are good group 65 car batteries in a cart I keep maintained, two are smaller Gold Wing size MC batteries, both those are AGM batteries. My stove is a VC Reliance, from 1992, but it seams to be vintage Harmon Accentra on the inside. Yes, distribution and exhaust fans and auger would use power ... as would the brain.
I have a 9600w generator on wheels that runs about 12 hours on 7 gallons that I used a few days in earnest in hot summer of '12 due to "the great derecho", then after back to normal changed oil & drained tank & carb, wheeled back into shop ... and a still new smaller 4000w that I bought on a super sale at NH one day to burn a coupon, I have yet to start it though. I did add wheels as it had none, but I lifted it into the trunk of my Mercury GM to haul home so it's pretty portable on wheels. It was bought as portable power. Both will charge batteries ... as will several Fords (why I have those two group 65s on hand). I have the transfer switch box, etc too.
Bought one of the small green 2 cycle portable generators for my brother in law and his wife to use at their horse-n-donkey barn that's 3-400 feet down a hill from the house, bought on sale at HF, and they have used the heck out of it I think, always attended when in use though, or so they say. Small and light = good for toting to the need. I don't recall wattage, but it likely would run a stove and reading lamp ok. Now I'm thinking.