For years we boondocked in our TT using 2 Deep Cycle 12V batteries and a 1000 watt honda to charge them with during the day. The generator would also run a small TV and VCR.
If we conserved electricity we could go for a weekend without having to charge the batteries. That meant turning off unused lights, using candles and trying to keep the water pump from running as much as possible.
The generator would stretch the trip out to a week or until we ran out of gas/water or holding tank space.
As others have said the 2000 watt will work well for you and is quiet enough not to distrub neighbors.