I'm a little confused as to what you want to do. Do you want a general use inverter that is not used often, but is available for things (like) your microwave? Or do you truly want a dedicated inverter to the fridge? In either case you will have to have a means to charge the battery bank, so you need an inverter charger - or a separate charger.
On trucks - that have essentially the same needs - we use a Kisae Abso 2000 watt pure inverter/charger with a transfer switch. It has direct wire capability, and a display panel that is able to be mounted remotely. It is well priced and pretty good quality. I've been using these for many years as the "reduced cost" inverter. It is not as good as a Victron, Outback, Magnum, etc but the reduced price makes it attractive, as does the feature set. They are well built and I doubt there are any more issues with them than any other line. I've probably installed 50+ of these over the years with no issues. Here is the one we use. LINK