I agree with worms. The best plant choices are things that are easy to grow, taste good, and are expensive to buy at the store.
For example, blueberries are a great choice to plant (though you're not going to get a blueberry seed for free). Once you've planted the bush, it essentially takes care of itself. You just need to cover the bush with a net just before the berries are ripe, or the birds will eat your harvest. They taste delicious, are easy to freeze, and they're super healthy for you. Plus, they're about $3 for a tiny tub at the grocery store, so your savings can be great.
On the other hand, potatoes are also easy to plant (you just need a plastic tub full of old leaves), but they're not going to be nearly as profitable for you: While they're filling, they don't bring a whole lot of nutrition to the table. And you can buy a big 5-lb bag for $2 or so; thus, your savings are minimal.
Dandelions? I wouldn't bother. How many would you need to make a salad?