I find that most of the time, carrots aren’t worth preserving because carrots are so dang cheap in stores. Same goes for potatoes. I reserve my energy for foods I can do a better job with than commercial companies or foods I can save a good portion of money with a couple of afternoons of work.
Jams and jellies are one of my favorites. I can usually beg some free fruit from someone (mother-in-law, mom, friend, national forest for certain berries) and then my costs are in the bottles I own, the sugar, the lids and the pectin. The jam I make always tastes better than buying and often I can save money by doing it myself. No money savings in concord grape jelly, however, I make it anyway because it tastes better. I find raspberry and some of the more rare berry jams save me money to make myself.
I do home canned green beans because I grew up on them and my mother gives me lots of beans every year, good Blue Lakes that are worth canning.
The one I’ve found the best savings with is the tomatoes. A small patch can produce huge amounts of fruit and a couple of afternoons is all I need to put up enough diced tomatoes to last me a year. I like it canned because most recipes I use call for canned tomatoes.
We also like to can juices. 100% juice is spendy at the store and I almost always get my fruit for free. we like grape and apple juice. It’s a bit more involved, but still an enjoyable process and the results are worth it because it tastes better than what I can buy.
I’ve canned chicken before when I got it for a really, really good price. That took a bit more time, but I loved having the pre-cooked chicken on hand for for things like chicken enchiladas, etc.
Preserving takes time and some funds. If you are canning you need some basic supplies. If you are canning things like green beans and meat, you will need a pressure canner. Those cost upwards of $70. Water bath canners run between $25-30. You need a jar lifter, jars (from $7-11 a dozen depending on size and type), rings, and fresh lids every year. Getting started canning is expensive, it’s the next years that you start saving money.
The only canning project I know that takes less than 2.5 hours is a single batch of jam. A smaller percentage of it is hands on; quite a bit of your time is spent just keeping an eye on the canner on the stove. Preserving food is time consuming. You need a day for just about any job you want to do. (Again, not jam. that can be done in a single evening.)
I’m not trying to put anyone off. Just go into it with your eyes open. Choose one food to start with and learn on. Work from there. If you enjoy it, add another food or two the next year.
I wouldn’t do it if I didn’t think it was worth the effort. Good luck!