Some inverters have an internal transfer switch. They function like a UPS - if grid (shore power) is available, it supplies the load. When not available, battery supplies load. If inverter doesn't contain it, then can be external (or use a battery charger as Supervstech says.)
More difficult is using up to 100% of PV to supply load plus additional power as needed from grid.
Without grid, up to 100% from PV and balance from battery is normal operation.
Once you size your planned system (Wh of battery, W of PV, W of continuous AC, W of surge AC), you can compare various AOI or individual components.