You dont need a big generator, I,ve programmed the inverter to limit input from the generator to 32amp . Its a 3ph generator used for running some equipment in my yard. Ive tapped off 240v from phase-neutrel. The only problem with tapping single phase off a 3ph is you introduce electrical imbalance, which is just as bad as mechanical imbalance. This is the reason I have limited the current draw from the inverter. Battery wise, I,ve gone with lead acid because Lithium are silly prices still. I think better and cheaper battery technology is very close and will continue with lead acid till then. As with all batteries, try no to over disharge them, size your battery so that you only draw down to 70% dod, your battery will last much longer. On average we are using 7kw hours per day. You can reduce usage from your battery by boxing clever. Only do heavy usage stuff while you genny is running. Ie washing machine, have a shower, boil the electric kettle, cook tea .....