For most people the 2 KW is the best choice. We have both a 1 and a 2 KW--Honda. We use the 1 KW on the CD 25 (didn't use it all last summer, but then we didn't use the airconditioning on the boat, except at the dock. There are plenty of places out West where AC is very nice. As I recollect at Petaluma I had the only boat with airconditioning--temp about 100 degrees, with high humidity. The 1 KW will run the WalMart Artic King 5000 BTU air condition, which fits nicely in the window of the C Dory 25 or 22. It will also run a 30 amp battery charger and a 600 watt heater (all we often need for the C Dory25 --but the Wallas, is more convenient), and one of the smaller "Galvez" microwaves. However, we find that most of the time, our outboard will produce all of the power we need for most uses.
On the Tom Cat 255, we use the 2 KW, because we have an 8300 BTU roof air, which is used fairly frequently, as well as a larger microwave, and it will run the water heater. We use the Garhauer davit to lift the generator from its box in the cockpit to the swim step and avoid back strain with that.
The Honda i series use a 12-15 volt DC primary alternator output, which is then taken up to very close to a pure sine wave 120 volt AC. So that even at idle they are producing 60 hz--and by my measurements and scope photos I have seen the power is quite clean on the 120 V AC power side--the 12 volts DC has some ripple between 12 and 15 volts.
We have used the Honda 2000 to run several refigerators during storms. But we have a 6.5 KW contractors generator, and a 16 KW natural gass pure sine wave generator for major power outages at the house--as Roger noted these are auto start and will carry most of the house loads. Things are cheaper in Florida--and the total cost was only $4700, including a solid concrete block base, 42" high, along with brick vinier and full autostart electrical pannel and gas hookup. (Fireman working on off days for labor). But we are in an area subject to relitatively frequent power outages.