Two very easy staple foods that I regularly make and use: labane (strained yoghurt), which will last a while if you roll it into balls and put in olive oil. Tahini - made from sesame paste, simply add salt, herbs, garlic, lemon juice and water. The paste keeps for very long, and you can use it in dressings (try it on roasted eggplant with lemon juice). There are strainers that allow you to germinate grains overnight, so you can keep dry grains (I use whole lentils, chickpeas, fava beans and dark beans), germinate them and keep them in the fridge for a few days. They go well in salads with lemon juice and semi-hard cheeses.
I've one uncle that makes olive oil, another ferments just about anything with sugar in it. Had some really good self-brewed beer once, but the person who made it told me you have to make it in large volumes, and I'm not much of a beer drinker.