Unfortunately, there is a lot of deliberately misleading advertising on most things you will find in the grocery store, because many phrases aren't regulated. For the record, "all-natural" means absolutely nothing. So how do you make sure you are choosing the best eggs? Better treatment of the hens leads to better, more nutrient dense eggs. So, let's start there... Here is what the different labels mean:
"Cage-free": Means that the hens are not being crammed into cages. However, even though they aren't in cages doesn't mean they are being treated well. They can crammed on top of one another in a single large pen but may never even be allowed to stop outside. No sunshine means no vitamin D. So, basically, these are not the eggs you are looking for... *imagine me doing the Jedi mind trick wave because I am a huge nerd*
"Free-range": Means that the hens are allowed outside, but this may only be for a few brief minutes every day. Again, same problem as with the cage-free eggs.
"Pasture-raised": Means that the hens live their entire awesome lives outside in an open pasture. More vitamin D and exposure to nature means healthier eggs! In fact, pasture-raised eggs contain 2⁄3x more vitamin A, 2x more omega-3 fatty acids, 3x more vitamin E, 7x more beta carotene, and 4-6x more vitamin D than the other varieties. These are the eggs you are going to want to look for at the market.
You will find that the healthier, more nutrient-dense yolks are actually orange.
You are also going to want to find eggs that are organic. This means that the eggs are not raised with antibiotics or hormones that can mess with your health.