welcome to the forum!
looks like you got a good start on electrical. there are a lots of good resources around to help you out.
everyone's system is unique, so there are lots of right answers. you have the pieces down. you need to calculate you loads, battery bank size, charging times with the generator, and how long you want to go on a charge.
with a big enough battery bank, you could go 3 days. a single battery is probably too small for that.
my house battery bank is 4 batteries X 110 AH each for a total of 440 AH. i use about 220 AH a day, so it works out that when i'm off of shore power, camping, i need to run my generator 1-2 hours a day to replenish part of that. lead acid batteries charge slow, so on a generator its hard to get them back to full charge.
so if i start out day 1 at 100%, morning of day 2 i'm around 50% and need to run the gen. the gen recharges that to about 80% for day 2, back down to 45-50% when i wake up on day 3, i run the gen for 1-2 hours and i'm back at 80%, until i can plug back into shore.
i also cook when i use the gen charging, so eating and charging go together. maybe an hour in the morning , and another hour in the evening.
solar would be a more efficient way of keeping batteries charged. if you are all 12v, you should look into that.
size your need in amp hours and go from there.
here is an easy load calculator:
i just re-read your post and you said roof top AC. that won't work on battery, only gen time. fridge needs to be on 12v battery.