I think this is an important question that can require some research and also some reflecting on your personal values, as well as your immediate priorities. There aren't easy answers, and the more you learn, the less clear some aspects will be. :)
Some benefits of organic produce/foods:
* non-GMO
* less environmental pollution and damage (though this can still be considerable, depending on the product)
* possibly less pesticide exposure depending on the individual food
These may or may not be priorities for you and your family. Notice that nutritional value is not on my list here. There are a lot of things that go into the nutritional value of a food. In my mind, freshness is the most important, followed by the soil health that the produce was grown in. Organic can have (but doesn't necessarily) better soil health, and may or may not be fresher. I don't buy the bell peppers that get shipped here from Israel in December, for instance, but I will happily buy the non-organic hothouse ones that are grown around here from March to October.
Personally, I would stick with seasonal eating first (for freshness), and then try to find sources of food in your area from farmers who are using organic or better (grass-fed, free-range meats for instance) methods, but who aren't certified organic. These types of sources tend to get you out of the industrial food industry quickly, and get you the most bang for your buck. Buy in bulk when you can; look for buying co-ops in your area. Watch grocery store prices and buy organic when it makes sense: when veggies and fruits are in season, there's often not too much of a price difference between organic and non.
Then let yourself off the hook. There is no perfect in this area; all of us are making the best decisions we can, and our economics and local resources are a part of those decisions. In my experience, getting too fixated on food rules is crazy-making.