If there's any kind of preserving I would recommend for anyone to start with it has to be dehydrating. It's really easy to do and even if you need some kind of dehydrator it doesn't necessarily have to cost a fortune to do a good job. There's some things you can dry in your oven or on top of your wood stove.
You can dehydrate fruit, herbs, vegetables and to some extent meat. We use small vegetables mixed together to make vegetable powders and that's one of the favourites in our family. We make a garlic powder that makes just about any dish taste marvelous. It might seem like a small thing to dehydrate your own herbs, but it's by far what we appreciate the most and everyone in our family use herbs and powders while cooking. I know my son's favourite is dehydrated spinach and I don't think he has ever eaten spinach before!
There's a lot of advantages to dehydrated food and surprisingly enough there's a lot you can do yourself. I think everything just tastes far better when you make it at home than the things you can buy. I used to buy dried bananas for our granola and I was stunned at how different the bananas were when I dehydrated them myself. Storebought bananas were hard as rocks, it's a miracle we didn't loose any teeth! The bananas we dehydrate are chewy and tastes more like candy than fruit. Dangerously tasty because you can't stop eating them once you start.
Some spices that I bought before are now replaced with homegrown and dehydrated herbs from our garden. I really like basil, especially in a simple caprese salad. I never had that in the wintertime before, the dried storebought basil tastes more like soap than basil so I usually just make it when I have fresh basil. Our own dried basil are something completely different. It stores up to a year before it starts to turn grey and the taste is so much more real than storebought.
Any dried goods have a long shelf life and it takes up less space. I store everything in reused glass jars, that'll keep it for as long as possible and it looks nice too.