Grade A is fine for use in baking or as an ingredient in a dish, but use AA eggs when you want a good-looking cooked egg. Eggs come in sizes from small to jumbo, which has less to do with their appearance than it does their weight. Most recipes in cookbooks are based on large eggs, two of which will yield a half-cup of beaten egg. For comparison's sake, it takes three medium eggs to get a half-cup. The color of the shell has no effect on egg nutrition or quality.
Brown eggs are laid by a different breed of hen than white eggs, that's all.
Egg yolks vary in color as well, from light to bright yellow. There is no difference in quality. The different-color yolk depends on what the chicken was fed. Buy the freshest eggs you can find. You should try to use your eggs a week or two before the date on the carton for the best freshness.