To solar or not to solar? That is the question....

If you choose the compressor fridge then battery and inverter is part of that project.

Solar just saves you the $2/hour(?) generator time. (fuel and maintenance). There is also issue of noise and convenience that is hard to quantify.

I recommend GoPower sine wave inverters. 1000w should be fine for the fridge. 2000w would be to run the microwave or some other heavy draw item.