Let's consider two seperate aspects of this thread (both related)
1) Battery Charging with a generator
2) Quality portable generators.
When it comes to a quality portable generator, you're going to be hard pressed to find one better than a Honda. Obviously, if money were no object, then installing an internal generator which is ignition protected, properly cooled and ventilated is the 'proper' way to go. However that is very expensive. since that is probably not an option, then one of your best options for a portable generator will be a honda. There is a more to the generator's than the label, Honda is not charging an additional $800 for the name.
when is comes to capacity, then work your way backwards with the generator being the last piece of the system.
1) How many amp hours are you typically drawing down on the batteries over a given time?
2) What is the total Amp Hour capacity of the batteries?
3) What are the type of batteries (flooded, Gel, AGM?)
4) What type of charger do you currently have installed?
-> Amperage output
-> number of banks
-> amperage draw
5) Now look at how long it would take for a generator to push the charger to recharge the amp hours drawn down.
I have 2 Group 31 AGM batteries and a Honda 2kW generator. The genny is bulletproof, however I have doubts it could completely recharge a single battery with a singel tank of fuel if the battery were deeply drawn down.
You have a main breaker as well as individual breakers for each circuit. If you're only running battery charger and fridge on the shorepower, I would assume you'd be safer leaving it connected, than leaving it disconnected and trying to recharge with the engine and generator alone. Also, most marina's don't want a generator running on the dock, so you'll probably only be able to run it out in a cove on anchor somewhere.