I have one Group 27 battery, and a 100w mounted solar kit from Windy Nation. It cost about $200.
I have dry camped for 9 nights three times, and never have run low on battery. Also have done two nights in a row, down below 15° F each night, and have used the furnace to keep at least 55° at night, and 70° in the evening.
I don't have problems with running low on power, even with furnace as only heat source. In my opinion, you would be fine with one battery, and at least 100w solar. Play it safe and get more wattage in your panels. Least-expensive way to go, in my opinion. If I wanted to spend more money, I would go with 2 6v batteries, instead of one 12v, though. May do that when this battery dies.
It was briefly mentioned, above, about draining your battery between trips. Parasitic drain killed my first battery after two years, before I got solar. Can't let it go dead, or you lose much of the storage power.
Good luck!