If you’re worried about being mean to animals and damaging the environment, figuring out what kind of meat/eggs/dairy to eat (given that you want to eat those things, which I do) is hard. Here is the simplest fastest #1 most useful rule: no subtherapeutic antibiotics.
Here’s the deal with antibiotics: they make animals gain weight faster. They also prevent animals kept in dirty, stressful, illness-inducing conditions from getting sick and dying. So confinement operations feed animals low doses of antibiotics all the time. As you might imagine, this is a brilliant way to develop antibiotic-resistant bacteria; in fact, it’s one possible source for the rise of MRSA.
Your solution: don’t eat meat that contains subtherapeutic — i.e. not for treating disease — antibiotics. Farmers who don’t routinely use antibiotics need to keep the environment cleaner and less stressful so their animals don’t get sick; they’re also not directly contributing to the development of antibiotic-resistant bacteria. (No antibiotics at all is ok, and a much more common label, but it gives farmers incentives not to treat sick animals.)
What to look for in the labeling: Anything labeled ‘organic’ had no antibiotics used at all, but some farms also label non-organic products as not containing antibiotics. Most of the natural, cage-free, etc eggs have that on their labels.