Fermenting: start with sauerkraut. Cabbage is easy to find and inexpensive, the only other ingredients you need are salt and time. Recipes are in every fermentation book out there.
Canning: whole peeled tomatoes are very nicely illustrated in the Ball Blue Book (a good starter book to understand canning process and safety). Canning whole tomatoes will teach you the basics, and it's best to start with an acid food so you are doing boiling-water bath canning instead of pressure canning. From here you can move into jams, jellies. Even easier to start is canning juice (like grape or apple) but tomatoes will likely be available sooner. Applesauce is one of my favorites for canning, no added sugar.
The very first thing I ever canned was apple butter. It was very easy to make and very easy to can.
To make: Basically, you just let apples and spices and sugar cook in a crockpot for a long time and then use a whisk (once they've cooked quite a bit and lost structural integrity) or an immersion blender to make them into a sauce and cook it all down to the consistency you want.
To can: Canning is easy because you do not need to pressure can this. Water bath covering the jars will do. I believe I did mine in a big spaghetti pot with one of those lift out sieves, and it worked quite nicely. It was only later after I'd convinced myself I could can stuff that wouldn't kill me or anyone else that I invested in the pressure canner.
There are tons of recipes on the web. If you find one that calls for apples to start with and not jars of applesauce, it's probably good. And apples are in no short supply here in western Montana in the fall. I'm guessing your markets are similar there in N. Idaho.
Also, this makes the house smell amazing, and it is delicious in a variety of ways. On pancakes, on toast or English muffins, in wraps, on pork, inside a grilled ham and cheese sandwich...
High acid foods can be canned without pressure-this is the boiling water bath method. Applesauce is easy to make. Peel em, core em, simmer till its sauce. Fill the jar, boil for half an hour or so. The Blue Book will tell you how long for the jar size at your elevation. Other high acid foods would include jams and jellies, tomato sauce/juice, and pickles of every kind. The big advantage of the water bath method is that it does not require a pressure cooker. A pot deep enough to cover the jar will work fine.
A note on applesauce:
While you can do it with a single cultivar, try mixing them up. Mix Macintosh with Red Delicious and Gala. Apples come in wonderful variety and they all have their own character when cooked into sauce. Some are sweet, some tart, mild, zesty, fruity, fragrant, soft, and firm. If you like chunky sauce, Granny Smith will hold up while Golden Delicious will be smooth. Tart does well mixed with sweet. If you go with all tart apples, you might want to add some sugar or cinnamon to take the edge off. With the right mix, nothing is needed but the apples. I've made excellent applesauce using crabapples in the mix. Come fall, you'll be hunting for those apple trees in peoples back fields.
Low acid foods must be done with a pressure cooker. The temperature must reach 240 degrees inside the jar. Since this is above the boiling point of water, it can't be done with the water bath method. Green Beans are pretty simple. Their shape and size is pretty uniform, and there is not a great deal of prep work; You can focus your attention on the process rather than the product. Cut or snap the ends off if desired, cut in half if you wish. Fill the jar, poke out all the air bubbles, process according to the Blue Book directions.
I agree with Joanne Daschel, sauerkraut is an easy project for first time fermenting.
Seed the Mind, Harvest Ideas.
my first attempts when I was YOUNG were things like a mixed pickle..which is a sweet pickle with pretty much any bits of this and that raw from the garden or farmer's market..it is so easy and delicious and uses the little bits that are available.
also I highly suggest jams and jellies if you eat sweet stuff, as they are amazingly easy ..and high acid foods are also so simple..like tomatoes.
you can also make recipes for things that your family may use on a regualr basis like tomato base sauces, ketchups, soups, etc..
and one thing that saves lots of $ is canning meat, does require a pressure canner but other than that it is one of the easiest things to do that will pay for itself well over ..by using on sale or home butchered cheap cuts of meat ..and you can use fish like sucker and salmon and lake trout too.
Bloom where you are planted.
Power corrupts. Absolute power xxxxxxxxxxxxxxxx is kinda neat.