Need help getting correct battery AH for off-grid

Thanks all! No fridge or CO detector will be used, nor will anything be used that needs propane or gas.

That was a good catch on the 600w inverter drawing amps from the battery. I had not thought of that :)

The only items connected to the battery (via inverter, and not all at the same time) will be:

2 laptops
Cell phone charger
Tablet computer
6" Fan
Hotspot
LED lights
Water pump (9 watt, 120v)

Now I'm leaning toward a 100AH AGM deep cycle.