Talk to some local gardeners about what they grow and what to stay away from. Assuming that it is veggies that your family likes, there is a starting point. Take some soil samples and take them to your local county extension office and get their suggestions on soil amendments. If you were in MO, I would suggest 8 mater plants, 4 zucchini hills, 4 squash hills, 4 pepper plants and 3 rows of corn for your first year (again, assuming that your family eats that stuff). A 30' x 40' area would be more than plenty for that. If you like cucumbers and/or pickles, I would expand into them on year two.
As far as the comment on all the work involved in gardening, if you don't enjoy being outside (some times in the sweltering heat), getting dirt under your fingernails, smelling like tomatoes, etc., etc., don't do it. It is work. That said, I love it. Planting the garden is some work (but to me is fun), but once it is in, you can fairly very easily keep up with a reasonably sized garden by spending an hour in it per night. For me, the real work is when you let things go for a week, then have to play catch up. I haven't been able to have a garden for three years, but for the ten years prior, I loved dragging the radio out to the garden, turning on a ball game and messing around in the garden for an hour or so in the evening.