I live without refrigeration out in Kansas, and we eat a lot of homemade pasta, pizza, stir-fry, dal, refried beans, and eggs upon eggs (gathered fresh and therefore kept at room temp). We dream of an icehouse, but for now we put most things that need extra coolness in a chest cooler (like you'd keep beer in at a picnic) and leave it outside by the back door.
Things we store in that cooler include:
hard cheesesgreensmisoyogurt (not in summer)milk (not in summer)leftovers (not in summer)
All our sauces, eggs, dry beans, grains, onions, spices, etc. are stored in our kitchen pantry. Fresh veggies we keep in a large bowl on the kitchen table, and use them up before they go bad. We just don't eat a lot of meat in the summertime, unless we only get enough to consume it all that day. In the past we have canned meat and made jerky.
I would like to learn how to put beef by in a crock under fat, like my great-grandma knew how to do.
Now that we are milking a cow, and are interested in making hard cheeses, we feel a fire under our butts to build that dang cellar and start getting serious about the icehouse. In the meantime, we make fresh cheeses in small batches, and eat them up before they go bad. One step at a time.
Meanwhile, I would recommend cooking seasonally. In winter, go nuts with meats and lavish casseroles and stews and pork pies and put it all out in the cold to keep. In summer, make quick-cooking things like fresh salads and pastas with pesto and stir-fries and miso soup and make only enough for one meal at a time.