The simplest solution is to purchase an inverter/charger with a built in transfer switch. You would connect your shore power cord and generator to one transfer switch and the output of that switch to the inverter/charger AC input. When it received AC power from either source it would pass it thru and charge your batteries. When the AC power disappeared it would supply your loads from the batteries.
If you want 1,000 watts and pure sine wave I would suggest a Magnum MMS1012.
I tend to think that a 1,000 watt inverter is an odd size. It's not large enough to run many microwaves, coffee makers, hair dryers, etc. However, it's much larger than necessary to run a TV, DVD, computer, etc. For the small stuff a 600 watt is usually plenty. For larger appliances a 2,000 watt is necessary.