My understanding is that there is a difference between free-range, organic, and grass fed. Free range is viewed as a more humane way to raise livestock--and I've heard some arguments that it improves the flavor of meat. Organic, as I understand it is more about no hormone injections, and that the animals are fed organic material. Grass fed to me mean that they are fed a normal diet for ruminants--meaning mostly grass and hay etc rather than corn, and other meals that are made with refuse from animal processing plants.
My main concern is that the health of the animal while living will directly affect the nutritional value when it becomes meat. I know there are people who have a problem with the medicines--but I think they are probably misinformed. I mean, its pretty important to medicate livestock, as livestock are the carriers of many diseases that affect human populations. However, when I can afford it, I do try to buy grass fed, free range beef. And pork and poultry that is fed their natural diets as well. Those usually come along with an "organic" label which if it means hormone free is alright by me.
As far as vegetables are concerned--I agree with most people here that pesticides are unavoidable--as are GMO's in many cases. Some things I will try to buy organic because the levels of carcinogenic pesticides used on them are at insane levels--like apples. What I have a problem with--and frankly everyone should--is monoculture growing practices. When crops are not properly rotated, and the variety of crops are limited by corporate farming practices, the nutritional value of the food is dramatically affected. To get the same amount of nutrients from an apple that you got from eating just 1 in 1940, you now have to consume almost 4. The same goes for grains and pretty much everything else we grow. Its difficult to say what can be done about it. I mean, if you have the time and space, grow your own for sure. However if like most of the people in the US you do NOT, then find out what you can to avoid the more harmful conventional items--like apples. Overall, as usual, I think the answer to clean, nutritional food, that also doesn't hurt small farmers, is a mass political movement that forces large growers to cease practices that are outright harmful, and eventually sets up a food system that can provide for large populations, but do not serve a profit motive.