“… This is a rare occurrence and doubtful that I’d repeat too often. …. I read I should get a deep cycle. I’d like recommendations for a good battery that will get us through a three day stay using the furnace, pump and lights. Installing multiple batteries seems like overkill if dry camping will be rare for us. …”
The size of the battery bank should be measured in amp hour capacity. Engine start batteries are rated in “cold cranking amps”. If the battery is not rated in amp hours, it is not likely a good deep draw battery.
For 12 volt appliances in a small travel trailer (you did not post model) to run three days, I use a pair of group 31 Interstate Marine 12 volt AGM batteries that are each rated at 100 amp hours. I get 3 days with good reserve capacity in weather with freezing nights and cold days. So this is the minimum deep draw battery bank size regardless of how often you use it.
You can get flooded cell batteries for less than AGM, but more maintenance will be required regardless of how often you dry camp. Water level must be monitored. Clean battery terminals and surroundings periodically. Remove corrosion and repaint battery compartment periodically.
AGM batteries do not require all that maintenance. However, they are sensitive to overcharging. Review your battery charger’s voltage profile when changing from flooded to AGM. My WFCO converter/charger works fine with AGM or flooded cell batteries.
“ … I’m going to buy a generator to recharge it daily. I’ve been talking for years anyways to buy one to help at home with occasional power failures. Thanks in advance.”
If you install 200 amp hours of batteries, you should not need a generator for charging. 200 amp hours will last 3 days. Recharge by plugging in at next destination. Charge for 14 to 18 hours for a full clean charge.
A 1000W generator is enough to run a 50 amp battery charger. You would need 2000 to 3500 watts to run 120 volt appliances while charging batteries.
A 3500 watt generator is probably too small for running a home. You could plug in a couple of major appliances separate from the home wiring system.
2 to 4 hours running per day would keep 12 volt things running. A full 14 to 18 hour charge is still required before storage. Always store lead acid batteries fully charged for long life.
Choosing An RV Battery https://www.irv2.com/forums/download...do=file&id=231
Note: The recommendation in this article to not use marine batteries does not apply to Marine AGM batteries. Large marine AGM batteries work as house batteries on boats and RV just fine.
Battery University https://batteryuniversity.com/
How does the Lead Acid Battery Work? https://batteryuniversity.com/learn/...ased_batteries
Charging lead acid batteries https://batteryuniversity.com/learn/...d_acid_battery
How to Charge and When to Charge? https://batteryuniversity.com/learn/...o_charge_table
How to Store Batteries https://batteryuniversity.com/learn/...tore_batteries
Summary of Do’s and Don’ts https://batteryuniversity.com/learn/..._battery_table
I wish you good luck and happy trails ahead!