Bob wells used to have a chart in his solar discussion that gave general estimates of what you could run off of 100 watt solar systems and 200 watt solar systems I believe up to 600 watt systems in I believe 100 watt steps years ago so you could get an idea of what you would need to improve to run more things. If I remember right a well insulated refrigerator along with a few lights and a fan were in the 200watt to 300 watt sections. I did exactly what you are planning to do except all I ran were fans, lights and 18 volt Ryobi tool battery charger and it worked fine for about 3 years before my marine deep cycle Optima batteries started not working as well. For me Optima batteries usually last twice as long. Without some way to bulk charge everyday and then allow solar through a controller float charge to full charge every day you will have shortened your batteries life in my experience and opinion. Most 12 volt compressor refrigerators have a low voltage cut off and after losing a bunch of food or worse yet getting food poisoning a few times then having to replace an alternator and a couple batteries because you failed to fully charge batteries a few days you may come to understand my views. If your plans don't include enough solar panels or a way to bulk charge a large enough battery bank I would use the batteries strictly for the refrigerator, especially if money is tight, as you can not afford to loose food or get sick. Good luck and remember results may vary!