We purchased our used Craftsman 5600 watt (8600 surge) generator on NHiMarket from someone in Conway for $400!! It is in great shape, and runs our house (a 2 BR ranch) without issue. Yesterday, we ran the whole house for 6 hours, and I mean the whole house! We have used it twice this winter. What a great buy. We had the breaker panel wired so we can just shut off power from the pole and plug the whole box right into the generator, flick a switch, and it's pretty slick! (Is this a "genset"? I don't know the lingo...sorry!)
I say it's enough power, the Honda you have...our 5000 watt has no trouble whatsoever running a house!