To offer a contrary opinion, our local master gardners suggest that private home food cultivation will never compete on cost with large scale agriculture. You pay too much for water, don't have enough land, don't get tax breaks or price supports, and can't reduce costs by using heavy machinery because your scale is too small. If it was really the most efficient solution, everyone would be doing it.
Maybe it's like homebrewing, where if you take out the logistics and taxes and don't pay yourself for your time it can be similar in cost or a little cheaper to the commercial alternative. Thinking of it as a hobby you don't lose much money on is probably a productive way to go.
"A hobby you don't lose much money on" is probably a perfect way to describe a home garden. I worked for 3 years as a county extension agent, and I've tended a garden nearly every summer of my life. It's fairly difficult for the home gardener to approach the costs of commercially-grown produce purchased in-season. I once owned a "free" tiller that my neighbor gave me, but I ended up spending more money trying to keep it running than it was worth. I ended up down-sizing and focusing on vegetables that gave us the most bang for the buck. That will be different for everyone, depending on what you like to eat, what you can get cheaply at the supermarket (or farmer's market), and what grows well in your region.
We found that in the South, it's hard to find a better bargain for your garden than peppers. Peppers are fairly easy to grow, and prolific producers from June until you get a hard frost (usually around Thanksgiving). We grew tons of bells peppers, banana peppers, and poblanos. Bell peppers are our favorite, but banana peppers are the heaviest producers and equally sweet when allowed to ripen. We didn't do much in the way of hot peppers - usually just one jalapeno plant and one cayenne plant - because a little goes a long way.
If you like squash and zucchini, these are tremendously easy to grow and huge producers, easily one of the best "bargains". They don't ship well, so they are expensive to buy at the supermarket. Make sure to get them in the ground early, because powdery mildew and squash borers will wreak havoc later in the season. Ditto with cucumbers (although they have fewer problems with insects). Our family, unfortunately, doesn't care much for squash/zucchini/cucumbers, so we never planted too many of these.
Tomatoes are another bargain, if you like to eat them fresh. I am a weirdo and only eat cooked tomatoes. My wife is the only member of the family who eats them fresh, so I always planted some for her and gave away the rest. I love my own tomato sauce, but canning your own tomatoes is an exercise in torture if you are as anal as I am and insist on ridding the sauce of all of the seeds. Plus, canning generally negates any cost benefit, once you figure in the cost of canning supplies and the energy to boil the sauce for hours on end. I just buy tomato sauce.
If you really want an efficient way to preserve your own harvest, freezing is the way to go. Legumes and sweet corn freeze really well. The problem is, they are difficult to grow in significant quantities on the cheap (ie, without a tiller and plenty of land). I usually just hoe up a short row to plant green beans, because we all love fresh green beans. Canning your own green beans will result in a fine product, but one indistinguishable from the cans that they sell at the store for $0.69.
Kale and broccoli are favorites at our house, and in our garden. Others cole crops are easy as well, but those are the only two that we eat. It's nice not having kale go bad - I just pick a few leaves when I'm in the mood. When we buy it, we always seem to waste some. Really, though, I don't think you're saving much, if anything, by growing your own cole crops. They are typically pretty cheap to buy, and unless you are growing your own from seed (which I recommend), the plants themselves can be expensive.
Veggies that generally don't make financial sense to grow yourself: Dirt-cheap stuff like Irish potatoes, carrots, onions, sweet potatoes. Not saying you shouldn't do it, just saying you're not going to do it more cheaply than you can buy it, unless you're growing on a very large scale.