Honda is ok...but extremely expensive compared to other options such as Champion.Honda is a good pick.. probably one of the best generators made. The different models in the same wattage are usually the result of one being a normal generator and the other being an inverter type.
Normal generators are more reliable, inverters put out a much cleaner power and use less energy doing it.
If you plan to use a generator to charge the battery, and it's only for emergency use, then you want to store your battery at only a 50% charge, and store it in a cold, but not freezing, space.
Of more concern is what inverter you plant to use to convert the battery power to household current. Morningstar makes very good products.. I can't speak for the chargeverter because it hasn't been out long enough to get a reputation yet.
You have a good plan..
I can buy two Champions for the price of one Honda with money left over.
I have run an inverter style Champion and and non-inverter style. The non-inverter has over 1,000 hours, and the inverter has almost 2,000 hours. The inverter has been used in show, rain, wind storms and generally abused. And it is still working as needed. My bad for abusing it...I was building a house at the time and didn't expect it to survive the 18 months...but it did and I am smiling for it.
I was very, very careful breaking them in and I used Lucas Oil Products 10063 Engine Break-In Oil Additive - Plus Zinc.