Is there a farmers market in your area ? When possible I try to shop locally and seasonal. Locally means grown in the area, seasonally means things that are in season. It generally means produce is fresher and hasn't been chemically treated in order to get it to market. This contributes to the healthy part of your request. I, personally, have issues with this whole, organic is better mindset. Think about it, organic ( other than pesticides ) means grown with organic fertilizer, manure or compost in most cases, and this is supposedly better using an argument that chemical fertilizers are deficient in nutrients which produces food that is nutritionally lacking. These claims are utterly false, ignoring the simple facts that if the soil is lacking in nutrients, the plants simply won't grow. It makes no difference whether the fertilizers are natural or chemical, plants will convert either to the same chemicals they need to grow.
Do you compare notes with the family, as to what they are going to purchase ? With $20-30 a week, you surly don't want to purchase the same things that you will have access to already. Look to supplement their purchases with things that are your favorites, like apples or fruits that they wouldn't purchase or veggies that only you like. Shop your local market and look for specials in the produce aisle. Get to know the manager of the produce department, they can really be helpful. When the Farmers Market isn't open, I shop one store for produce, the manager knows that I am loyal and points out what's the freshest or grown locally or he will tell me if something is getting old and I should stay away from it. He turned me on to some locally grown sweet potatoes, that he carries that are hands above any that I have ever had.