I would stay away from canning pesto or anything with oil, due to the high botulism risk. Also, properly lactofermented foods will stay good for a while.

To can low-acid foods, including tomatoes, you will need to invest in a pressure canner. Personally, I like the canners at Lehman's Non-Electric. They're amazingly high quality and even though they seem expensive, they'll last you DECADES!

For canning high-acid foods (many fruits, etc.), you can use a water-bath canner, but in my experience, it's a waste of time if you have a pressure canner. Everything cans better in a pressure canner, and the process is shortened substantially using a pressure canner, so I just use mine for EVERYTHING!

Then, you'll need canning jars. Quart jars work well for broth, meats, and marinara sauce, etc. Pint jars are nice for things like ketchup, as are half-pint/jelly jars. You can pick them up in a LOT of places.

You'll also need a good "canning bible". I strongly recommend the "Ball Complete Book of Home Preserving"; "Homestead Blessings: The Art of Canning"; "The Home Preserving Bible"; and several sections of "Nourishing Traditions".

There are some other tools that are really helpful -- a good ladle, wooden spoons, "bubbling spatulas", a good cooking thermometer and candy thermometer, good hot-pads, a cooling rack... but you'll learn about THOSE in the canning books.

I support you in learning to can food, it's a great hobby and way to preserve the harvest. I have been on both the giving and recieving end of various homemade canned goods, and I know from experience that these often go unused. Whether its because the item is an unfamiliar food, lacks a bright shiny label when you go in the cupboard to make dinner, or even the fact that some people are suspicious of home canned goods and fear food poisoning (esp botulism) they tend to sit around until they really are to old to be good anymore. Yes, there are exceptions to this, my mother in law loves my pickled beets and I enjoy my sister in law's salsas, but in my experience any kind of food gift- jerky, nuts, cookies etc will be consumed and enjoyed- whereas canned goods tend to sit around. My mom is actually scared of home canned food, and sadly she is not alone in this. Canning is fun and creative but it also involves a big expenditure of time, energy and an up front investment in equipment. Not to be a Debbie downer, just what I've noticed over time. If you do make things to share with others, it's important to clearly lable them with all the ingredients. I once opened a jar or relish I got in a local canned good swap to find it was syrupy sweet and full of my enemy, the only vegtable I will not eat, green peppers. Labels will help make canned goods less mysterious and up the probability that they get eaten. I highly reccomend getting the Ball Blue Book and taking a class from your local co-operative extension when getting started. Good luck!

There are other methods than canning, it would be worth perusing a copy of

Preserving Food without Freezing or Canning: Traditional Techniques Using Salt, Oil, Sugar, Alcohol, Vinegar, Drying, Cold Storage, and Lactic Fermentation

we use certain types of preserving presented in the book quite often.

Additionally, we use a lot of drying.

We do can a fair amount, but generally limit the high sugar canning segments. We try to balance the amount that is canned as we have a certain amount of "rawism" in our peculiar paleo variant!