A cheap and easy way to get the fresh vegetables you want is to grow your own -
You can get a young tomato plant for $3, stick it in a hole in your yard, and get up to 20 pounds of vine-ripened tomatoes (currently going for $2.49 a pound at Wegmans) in a year... as long as you don't let it die.
Don't worry, gardening isn't as hard as it sounds. While it's a lot of work to maximize yield, it doesn't take too much to get productive plants. One easy way to get started is to grow plants in containers or bags. The cheapest way to get started this way is to buy a bag of topsoil and plant directly in the bag. All you have to do is lay the bag on its side in a place where it can get lots of sun outside, then cut holes or slits in the top side to plant your seedlings or seeds in (make sure you follow the instructions that came with your plants!), then poke holes along the bottom to let water drain. After that, just check your bag every day to make sure that the soil is damp without being muddy, and add water as needed. Don't worry about pesticides or fertilizer to start with - blemishes on vegetables and holes in your greens won't hurt you, and your bag of topsoil will have enough nutrients for one year. I don't use any chemicals in my garden, so I'm getting homegrown organic produce for bargain prices! Yum!
Do beware of larger pests like rabbits, groundhogs, and deer. While insects won't eat everything (unless it's a swarm of locusts), these evil mammals can eat entire plants in one go. If these guys show up, you can either move the container to a sunny porch (and hope that they aren't so daring as to come right up to your front door!) or you can put in a fence. Throwing rocks work if you catch them in the act too.
So what should you grow? Whatever you want to eat, of course! Some vegetables are harder to grow than others, but you can figure it out just by reading the instructions that come with the plants. Common garden vegetables that are recommended for beginners with containers are tomatoes, peppers, eggplants, squash, bush beans, and peas. Other plants like leaf lettuce and radishes are also good growers, but I don't recommend them because they're already so cheap from the market anyway. Google is your friend for ideas here.
