Help on an Inverter/Generator pair for a semi-off-grind Cabin :) (USA)?

Not sure where to ask this, but we are looking into building a small cabin for our permanent living space.

We are looking for an inverter/generator that we can hook up batteries and future solar panels to and it also be connected to the grid while we are setting everything up/building.

Does anybody have any experience and want to give me suggestions on the type of equipment to do this?

The types of generators I'm seeing ATM output AC power (have their own inverter) and I'm not sure how I would use something like this in the system.

Something like this schematic shows an inverter that can take both AC and DC power, but I'm not finding anything that seems to fit that bill.

I would imagine we want to spend the most on the inverter to future-proof our needs, and a good enough generator to supply the surge/max-wattage of the inverter if the power of our city goes out (or at least enough to run a fridge and/or power tools while we are building)

Edit: Something in the 5000-8000W range would be enough for our needs. If you have any battery-bank suggestions (I can only find a max of 100Ah batteries) that would be great too.