Id suggest the Honda eu2000 for its history or reliability over any other offering.
Do careful price comparisons vs. multitudinous 'dealers', including internet sources, as the prices (and taxes, plus shipping) will make a BIG difference.
A 2000w generator will 'run' most household 'load' such as heater, lighting
, refrigerator .... but not all at the same time because of the 'starting torque' requirements of 'motors'. This leaves only well pumps
and other 220v components/requirements not able to be supplied.
The 1000w, simply doesnt have enough 'umpf' and the 2000w will be mostly 'above automatic idle'. You really dont want to be running such equipment 'flat out', as this 'kills them quick'.