I think you could run 6 volt batteries from Sams club about $85.00 plus core charge. You will basically be fine if you start off with 2 6 volts and add as you learn what solar system etc you need. To charge the battery quickly I would not rely on the house converter. Get a real battery charger. Right now your house converter changes 120 volts ac to 12 volts dc to run things and it charges your battery. Converters are often not the best battery chargers, especially if you want it done quickly. Read up on proper charge voltage and equalization/sulfation. Your house batteries and solar batteries can be the same. The coach chassis battery will be just for starting the motor home.
Go to all led bulbs from ebay or amazon. Don't pay big money for them. Your house furnace will use the most battery power. Try to not invert as inverters use power in the conversion process. We could talk all day but there a very knowledgeable guys in here so read a lot. You could probably start off with a relatively small generator and a good charger. The solar gets into issues like stationary vs tilted vs manually aiming them at the sun. I'm learning more about that myself so I cant help much. What state are you in.
