Use a "hybrid invertor" and deep cycle lead acid. Since you're feeding it with electric service you could use one designed for RV/boat shore power. These start at about $3k.
Or you could just run everything off an inverter non-stop and keep your batteries topped up with a DC converter designed for RV use. That would be the cheaper option.
A combined inverter/charger will switch from.external ("shore") power to inverting from the battery, but make sure the switch will be fast enough to keep the printer running. I was doing this 20 yrs ago, and the switching was not fast enough to keep my computer running.
The hybrid inverters are pretty good now. They sync with shore power and soft switch.You can run large appliances such as an electric stove while the RV is only connected to 15 or 20 amps. It will draw from the battery to help supply the load and then charge the battery when the load is low.
(post is archived)