I'd go with the Honda first, then solar, just because there may be times where the batteries need a charge to handle the furnace on a cold night, and it is coming evening time.
Even with an inboard generator, a little 1000/2000 watt inverter generator comes in handy, just because they use far less gas, and if charging batteries for a while, might as well use something that uses 1/10 of a gallon an hour than something that uses .4 gallons per hour. Plus, there is always that time where the house batteries can get so low that the onboard Onan might not be able to start up, so having a backup on hand can save a trip.