Selection of inverter is depend on the requirement at home, for exam.
If grid supply available at home and want to use solar as backup and reduce the electricity bill without storage of power and low cost use ON Grid Inverter.
If Grid supply/connection not available at home & storage of power needed during unavailability of solar means battery connection required, use OFF grid solar for Home.
If the power requirement small, only to run small application like one or Two CFL connection and One set of fan, than can use Hybrid or micro inverter for such small application.