Before deciding on the inverter size, you need to figure out the AC watt-hours you'll use up before you get to recharge the batteries attached to the inverter.
Watt-hours is simply the sum of each AC load you'll have in watts times the number of hours you have that load. Then you need to find the DC amp-hours that represents.
You convert the AC watt-hours to DC amp-hours by dividing total watt-hours by 10. For example, if you plan to use 1000 watt hours, that's equivalent to 100 battery amp-hours. (Since it's a 12-volt system, you'd think you'd divide by 12, but dividing by 10 adjusts for the inefficiencies in the conversion.)
It'd seem like you'd then need 100 amp-hours worth of battery bank, but you want to discharge your batteries only 50% AT THE MOST, and 60-70% would be better, particularly if using lead-acid batteries. So you'd need a minimum of 200 amp-hours of batteries to cover the 1000 watt-hour load.
In addition, to make sure your batteries last for years instead of days, you have to limit the discharge rate to a certain percentage of the capacity. For lead-acids, you'll kill them off if you routinely draw off more than 25% of their amp-hour capacity. With our example of a 200 amp-hour battery bank, that means a maximum of 50 amps draw, which is (at 12 volt with inefficiencies) about 500 AC watts. Fortunately, AGM batteries are OK with 35-40%, which means as much as 800 AC watts available at a time.
Anyway, you can find more cogent and detailed explanations of this stuff all over the internet, but the overall point is that the size of the inverter isn't all you need to know, since a big inverter with a small battery bank is not going to work for you.