Yeah,a single Grp24 battery will probably be a problem with a lengthier stay. If you do install 4 GC2 6V's you'll have a lot of capacity, probably enough to overnight for a couple of days. We don't know your exact usage, i.e. running a furnace for heat uses a lot of 12 V power.
The built in RV converter should be a good charging source and operating a generator is a good time to use that available 120V AC. You could post up the converter model numbers for more focused advice. You can also use a stand-alone battery charger at the same time to limit generator run time. Assumed that the two charging devices charge the batteries quicker, together.
The yellow Champion generators are a good buy, IMO. the Honda and Yamaha inverter generators are at the top of the list and have prices that match. I'd avoid Costco WEN generators or Harbor Freight knock-offs. Serviceability is questionable about those latter ones.
If you have plans to camp off-grid occasionally, solar panels are like peanut butter and jelly with 12V systems. You do have to get Sun on them but a generator for back-up use is a good plan.