CatEyes

IMO, don't fall for the carrot.
Bought 2 recent LFP batteries, one from LBSA and the other from Volta.  Both 1C charge and discharge (100A) batteries.
Volta looks good, come with DC cables, but don't have DC cut-off switch and don't come with a LCD screen and menu buttons.  Bad customer and back-up support.
LBSA, local manufacturers of system, very good local support and they call YOU back !   Battery come with DC cut-off switch and LCD screen en menu buttons.

My BEST experience. We repair a power supply where a staff member of a company reversed the polarity. 20min the same PSU came back with another reverse polarity with the PCB track just burnt more. 

Hi CatEyes, welcom to the club.
Taking in account the simultaneous factor (not all families do the same thing at the same time) you do not have to add up the full peak power. Give it 80%. That's the advantage of one system for them all.
Second, consider at least 2 parallel units for redundancy. I would rather go for 3. In case one fails you would still have 2/3 of power available. That's the other advantage of one system for them all. It's part of your liability to the dwellers for reliable service. I.E. 3 4kW or 3 5kW units.
And of course, as mentioned by others - batteries, batteries, batteries! If you conceive only as UPS for LS you may get away with 20kWh (400Ah). If you think of getting off grid with solar, then you would need lots more.

I haven't mentioned batteries since I only wanted to find out about the inverter sizing.
Adding additional batteries and panels later is always an option since someone will find a use for the extra capacity but having to buy an additional inverter just because you spec'd the system 1kW too small for every time grandma makes a cup of tea is going to be expensive.