Welcome Hawaii Hank!
Check out the FAQ pages, they'll answer most of the upfront questions you have. To power a refrigerator and led lights you need to know how many watts they consume in a day. That'll give you watts/d. Then you need to make a guesstimate for how many days of shade you'll have to oversize your batteries. Same concept for how many watts of panels you need. But...go through the FAQ and then come back with specific questions as those will be a lot easier. There are also a number of examples that folks have put together you can find by perusing the forums.