A 500 watt inverter that plugs into a cigarette lighter will work, and only cost $40. You can install several cigarette lighter receptacles in the RV and use the small inverter anyplace you might need it. I would wire it up with #10 wire and a 20 amp fuse. While only good for about 250 watts, you probably will not use more than that anyway.
For solar panels, contact this place, and look for 12 volt 'nominal panels' that are 20.5 to 22 volts open circuit. And a PWM controller. They are fairly low cost, I bought a 10 amp PWM controller for about $20 last summer.
SolarElec.comFor mounts, I suggest 6" long of 2" angle aluminum from Home Depot. Drill 3 each 3/16" holes for #10 screws into the roof, and 5/16" hole for the 1/4-20 bolts into the solar panel framework.
I ran #10 romex direct burial wire through the refrigerator vent to my controller, then to the battery. (Home Depot).
I started with a pair of 45 watt panels (in 1994 it was a good cost for $750 to buy the kit, along with mounts, instructions, and wire.)
I installed a 75 watt panel ($375 at the time) in 97, and pair of 120 watt panels for $429 each in 1999. Now you can buy a 100 watt for about $100 or so.
I would recommend at least 200 watts. Your RV will consume 35 amp hours daily just running the CO and propane detectors, along with the refrigerator. Add the 30 amps that the furnace can use in 24 hours, and 10 - 15 amp hours for lights, 20 - 50 AH for computer, TV and Satellite dish, you get a total around 120 amp hours for my system, and I could make up that much power on a short 9 hour day in November.
If you like 200 watts, you really would like 400 watts, and probably would not need to run a generator. 600 watts, and you will not need to be conservative with the lights either!
I have a Olympic Catalytic Safety Heater, and it does not use any 12 volt power, totally silent, and you need to leave a roof vent open about 1/2" and window open a little too. Just like burning gas on your stove, you need to leave a window and roof vent open. The 6,000 Btu keeps my 30' Bounder toasty warm at 19F outside, with only a little furnace run time each night.
Good luck!
Fred.