Am_Fear_Liath_Mor makes a good point.

Running a household AC powered fridge via inverter and battery is not a good idea as the amount of stored battery power to even run an AC fridge for a day is financially impractical.

If one is looking to have a fridge for power outage use, then searching Craigslist for used dual 12 volt / propane powered RV fridges is a much better option. The fridges come in all sizes but of course will not replace your household fridge capacity wise. However they will have enough room to keep some milk and other perishables on hand.