First of all, when on shore power it really matters little what type or capacity battery bank that you have. The battery is there for things 12V & the converter/charger will keep the battery topped up.
If you are one of those who only uses shore power you might as well buy the cheapest, smallest capacity battery that you can find. It is only when you get into the dry camping world when you need to think about battery bank capacity & type of battery. It can be the cheap wet cell, common starting type or deep cycle or graduate up the line, & expense, to AGMs, gel cells or Lithium.
A fridge on shore power does not care what type of battery is installed.