mterle, This is tricky. Here are some rough numbers from :
A 12 volt 100Ah deep-cycle battery with regular depth of discharge 50% would run a fully-loaded 1000 watt inverter for 34 minutes. This calculation takes into account average pure sine wave inverter efficiency of 95%.
The easiest way to calculate 100Ah 12 volt deep-cycle run-time is to convert the amp-hours to watt-hours. Simply multiply available Ah by the battery voltage to find its watt-hours capacity:
Battery watt-hours = amp-hour capacity x battery volts
Battery watt-hours = 100Ah x 12V = 1200 watt-hours
If you are using 1000W you'll really need a full on system of some sort with likely at least 4 12V deep cycle batteries just to run things for a couple hours. Then you'll have to charge them with panels or a generator.
I'd opt for the low power route and make that tradeoff but that's just me. Big loads are expensive and get complicated to build in that capacity unless money and space don't matter.