"Organic" is probably the most generally reliable label for beef, pork, chicken, and produce. The USDA organic standards describe how farmers grow crops and raise livestock and which materials they may use, favoring methods that preserve the environment and avoid most synthetic materials such as pesticides and antibiotics. So when you buy "organic beef" or "organic chicken," you can be relatively certain federal inspectors made sure it wasn't raised using bio-products, hormones, steroids, or antibiotics.
"Natural" is a different story. The USDA's definition of natural is so broad that it literally includes every single animal raised in the country, no matter what it's fed. The term "grass-fed" is also misleading: consumers see "100 percent grass-fed beef" and assume it's drug-free, but that's not true at all.
One of the safest and cleanest meat options is bison. So far, bison production in this country is all drug-free. It used to be a specialty product, but now you can buy bison all over the country in grocery stores and many restaurants.