It would be easy to calculate the size of the inverter and amount of batteries you need. All you need for this is the amp rating of all the equipment you want to run at the same time and for how long. Based on that you can determine the wattage of the inverter and the amount of batteries.
We have a thing called "Loadshedding"here by us. Basically our power utility can not supply enough power for everyone in the country during peak times, so some people get cut off to keep supply and demand balanced. It is on a rotational basis. So, if you want the lights to be on during your turn, you have to provide your own power. We are pretty good at calculating what we need to keep the lights on by now.
You get me the info on all your equipment and I will give you the answer, unless you go Google it. The info/formulas is out there. You might also know an electrical guy that can calculate it for you. Hope it is a one night stand thing, because if you want to solar charge it for a second night, that is another story. But you could then use your generator with a standard charger, which would be cheaper.