Odyssey or Northstar Group 31 AGM batteries, 3 or 4 of them In balanced parallel with 00 gauge ( or fatter) interconnects . These thin plate pure lead batteries will hold higher voltages under higher loads than other AGMs. They can handle, and actually require huge recharging currents when depleted to 50% or below.
2000 watt inverter of your choice.
Power this charger with the Honda 2000:
http://powermaxconverters.com/product/pmbc-12-volt/
They go as high as 120 amps. At a minimum, get 30amps per 100Ah of battery capacity, Odyssey....40amps.
They have an adjustable voltage option.
Use a short length of no thinner than 4 awg to powermax
Northstar wants 14.46@77f
Odyssey wants 14.7v@77f. Odyssey dictates that when deeply cycled it requires a 40% charge rate, 40 amps per 100AH of capacity.
With batteries at 50%,
Set charger when unloaded ( not hooked to batteries) to ~0.15 V more than above voltages, adjusted for temperature. Higher battery temperature lower voltage, lower temp higher voltage.
mark/note position of voltage potentiometer.
Warm up honda 2000, plug in powermax, hook to batteries on opposite end of the string(+) on battery 4, (-) on battery 1.
Flip switch on.
Once the battery terminal voltage hits the desired absorption voltage which will take about 1.5 hours on 300AH with a 120 amp charger, you might want to back off the potentiometer a smidge. Hold desires absorption voltage for ~3.5 more hours minimum, before these batteries can be considered fully charged. Really once amps taper 0.5 amps per 100AH of total AGM capacity at absorption voltage, so an accurate ammeter is required to truly know when these batteries are full.
http://www.amazon.com/DROK-Digital-...id=1462507045&sr=1-1&keywords=200+amp+ammeter
But these are not very accurate at low currents.
A clamp on DC Ammeter can also work for measuring when amps taper to 0.5% of total capacity at ABSV.
http://www.amazon.com/Craftsman-Dig...&qid=1462507336&sr=1-7&keywords=clamp+ammeter
Shop around spend 35+$, make sure it can measure DC amps as well as AC, cheapos do only AC
Like all lead acid batteries, they require a true 100% recharge every so many deep cycles, or they will lose capacity faster.
AGMS seem to lose capacity faster when not returned to 100% more regularly, and all of them enjoy higher charge rates, upto 30% on the lower end AGM, and no upper limits on the Lifeline/Northstar/Odyssey AGMs.
When the AGMS get beat down from many cycles without a full recharge, one needs to do the high amp recharge from 50%, and hold absorption voltage until amps taper to 0.5% of total capacity.
This might take 10 hours or more!
With the last 1% taking 3.5 of those hours, so even smaller amounts of solar, once it along can maintain the few amps needed to hold absorption voltage can really help reduce generator run times, and also slightly lessen the load on the batteries around solar noon.
If you go with less expensive AGMS like Deka Intimidator( oft relabelled sold in sams and costco), get another 100Ah capacity so as not to exceed a 30% charge rate on them.
Even if you can't run the generator and hold absorption voltage as long as might be needed/ desirable, 300AH+ of TPPL AGM batteries will gobble everything up that a 120 amp charger can produce, the Honda 2000 'Should' be able to power it.
The key to getting your money's worth out of 1000$+ of lead acid battery in your stated usage, is get the batteries to ABSV as fast as possible, and hold it for as long as you can. If you can hold it until the solar can maintain 14.4 to 14.7, and the solar holds it 1t absorption voltage the rest of the day, all the better.
The reason I recommended a Manual adjustable voltage charger/converter, is because the automatic ones might not hit the right Absorption voltage for the battery, and its temperature, and they certainly will not hold ABSV for the time needed. There is little point in running the generator when the charging source prematurely drops to 13.8 volts automatically. Intermatic sells wind up timers, get a 6 hour one and then no real fear of overcharging.
The Powermax converters are also power factor corrected, meaning they are more efficient. 120 amps on a standard 15 amp household outlet. other brands require a 20 amp outlet for ~80+ amps.
If you get enough solar that can still seek and hold absv when an automatic converter reverts to a lower voltage, that works too, but the solar controller would then need to be programmable too so it can hold absorption voltage instead of the premature float that is so common.