I can, freeze, dehydrate all sorts of produce that I have grown in our gardens. I would highly recommend that you purchase the "Ball Blue Book of Canning and Preserving". It is an excellent resource for those who are new to canning and freezing and gives you step by step instructions as well as suggestion/recommendations of equipment that you will need. There are excellent recipes in the book too - you can follow them, or alter them to suit your diet needs. There is a section in the book for diabetics as well and will give substitutions for splenda instead of sugar.
I typically freeze a lot of veggies as I like them a little more crisp than what canning (water bath or pressure canning) leaves them. I clean the veggies and blanch them in boiling water for a couple of minutes and then dunk them into a ice water bath and then drain/dry the veggies before I put them in freezer bags or in my vacuum pack food saver. The blanching process allows for the veggies to keep their nice color as well as allows for freezing without a lot of freezer burn. There are a few veggies that if you want to can that you will need a pressure canner rather than a water bath canner. It is very important to portion control what you freeze too. Some items I put in gallon size freezer bags, but the majority of the veggies I put in quart size.
I freeze asparagus, broccoli, peppers, onions, carrots, green beans, peas, spinach, swiss chard, sweet corn, and cauliflower. I also freeze berries and other fruits that we grow.
I dehydrate all of my herbs, onions, peppers and make my own fruit leathers as well.
I can jams, pickles, beets, apples (apple sauce, apple butter, apple pie mix) as well as make my own fruit syrups for ice cream, cakes & pancakes. I also can a lot of tomatoes, tomato sauce, salsas, and make my own spaghetti sauce and chili sauce to can.
I do not can any meats.
This is A LOT of work, but so worth it in the middle of winter when you get out a bag of frozen veggies, or a jar of homemade jam. After the initial purchase of equipment, jars & bags that you need it is also very economical to preserve the foods that you grow. I know with all of the problems with the produce in the country I feel safer feeding my family items that I have grown as well.
The first time I canned pickles, I canned a lot and had too much still left by the next growing season. I typically only keep for a year, so I do plan on what we will eat as close as I can for 1 year. Items that would have multiple uses like tomato juice I can a lot of. It can be used for spaghetti sauce, chili, tomato soup, veggie soup base along with chicken stock, etc. I make a version of my own V-8 as well, but without all the salt.
I will also make my own stewed tomatoes - I will add that to chilis, spaghetti and soups. I have cooked the stewed tomatoes and put portions into ice cube trays and then popped them out once frozen and put them in freezer bags. Then I just grab one or two of those to add to soups or stews.
You will also need a place to keep all of your canned goods. It is best in a cool, dry place that won't get sun. We have a room in our basement that my husband built shelves in for me that we store our produce in.
As you can tell, I love to garden and preserve the foods that we grow. If any of you have any questions feel free to PM me and I will answer any questions that you may have.