Store bought eggs are fine, but eggs from true free-range chickens are usually more nutritious than commercially raised eggs, with better fat balances and more vitamin E. You can find these if your neighbor happens have chickens and has more than they can use–or you can buy them at a all-natural food store sometimes, like Sprouts, Wegmans, or Trader Joes.
Some prefer the egg whites, some the yolks. If you re looking for less fat, use just the whites. For more calories, add the yolk. Some even recommend feeding it with the shell on.
Some researchers are concerned about a substance called AVIDIN contained in egg whites. It is thought that it interferes with absorption of the biotin in the egg yolk. Cooking the egg whites will prevent this problem, but changes the structure of the proteins in the egg whites. Some other researchers believe that it is not necessary because the yolks have more biotin to overcome the biotin loss, so I recommend that you feed them raw. Cooking the yolks, in addition, significantly reduces the lutein content. Lutein has been reported to be a very important nutrient for the eyes.
One of the reasons people leave the shells on is that the membranes in the shell contain glucosamine, chondroitin sulfate and hyaluronic acid—nutrients reported to help relieve joint and soft tissue pain. Fresh eggs also provide important brain, eye and other body nutrients in natural, unprocessed form such as riboflavin, magnesium, potassium, selenium, and zinc, and Vitamin K. Egg yolks contain essential fats, including linoleic acid, phospholipids, choline, lutein, vitamin D and E. Furthermore, they contain cancer-fighting gamma tocopherola and toctrienols. While egg shells provide a source of calcium (if washed and fully ground), they are not really necessary.