It sounds like you will do a long term cruising trip of a month or more. In that case a solar panel system will probably be better as it takes no attention.
I wrote a three part series of articles on solar power that you can download from the Forum's library: Trawler Forum - Library - Systems
. Start with the one on sizing which looks at battery capacity, usage patterns, etc. Then read the one on installing a large solar panel system. If you do it yourself you can install a 3-400 watt panel system for the cost of the Honda.
If you decide to use a Honda generator, think about how much current your shore power charger draws. A 100A charger often draws 15+ amps at the beginning of a charge cycle and that is too much for the continuous rating of the Honda 2000. Newer 2,200 watt ratings from Honda and Yamaha may be able to handle it though.
Also for charging batteries powered from a generator you do need a decent sized charger. Trying to charge a 220 Ah bank with a 20A charger will take a long generator running time and won't be very efficient.
As noted above, an intermediate system would be a Honda generator, powering a decent sized shore power charger with a 100 watt solar panel to top off the batteries. Look at my first article "Solar Panels for Your Boat" which discusses small solar systems. A 100 watt panel can be installed yourself for about $200.