I think the term you're looking for is "homesteader", as opposed to farmer.
Farming is a tough, tough industry. Lots of risk, little reward. To really compete and earn a upper-middle class living you have to have a huge mechanized operation, employees, lots of stress, capital investment, etc.
So, the homesteading option allow you to focus on 2 things: 1) reducing your living expenses, and 2) earning a bit of extra cash. What it effectively is is a part-time job. So, you have to really enjoy all the activities. Money-wise, it doesn't make a huge amount of sense, but if you enjoy it, then it's a great, fun hobby with a positive economic side. If you're looking at it purely from the POV of economics, it's a demanding job with really crappy pay.
The best thing economically is the potential tax savings, depending on your current income level and tax rate. If your marginal tax rate is 50%, then to buy a bag of potatoes you might pay $10, meaning you have to actually earn $20 to buy them. However, if you grow them yourself, you pay nothing, and don't have to earn the $20. Also, if you actually do some of it for profit you open up the small business tax credit side of things - but not an area I know much about.
So, dip your foot in slowly by planting a small garden. Do NOT get any animals at this stage - too long of a commitment. If you end up liking the gardening, try meat chickens - they are only are around for 8 weeks, but they are unpleasant and don't save you any money. The meat tastes better though, as it has actual texture and more flavour (assuming you let them "run" around the yard and eat bugs... "running", in the case of meat birds, consists of waddling a dozen feet and sitting in the shade all day, pecking at bugs if they happen to run by).
Build it up over time. If you get to the point where your job becomes a distraction, and you've managed to generate a good income, quit the job. But don't jump in with both feet.