Whole grains are better for you. They contain many more nutrients than more refined flours because most of the nutrient content is in the germ and the bran. The best kind of flour you can eat is flour that was ground less than 24 hours ago. After 24 hours the nutrients start to die off due to oxidation, (exposure to air) and the longer a flour sits on the shelf the more it resembles glue paste and the less it resembles food. I know a lot of families who have a grain grinder and bulk order buckets of whole grains that they grind in small batches so they always have fresh flour for baking. Not everyone can afford to buy a grinder, like me. (I can borrow my MIL's though, and do often.)
What the rest of us can do is this. Check the dates on the whole wheat flour you buy at the market. Try to get it as recent as possible. Keep your flour in the freezer to keep the oils in the germ from going rancid. If you can't find whole wheat flour at your local store, you can either talk to the manager and request that they keep some in stock, or you can start looking around online and order in bulk. If you live anywhere near where grain is grown, find out where the grain is milled and stored and buy it straight from there. (My grandpa is a farmer so we got all of our flour this way, from his fields.)
One flour that I like to use is King Arthur Flour white whole wheat flour.
Not only is it free from bleaches, bromates, and chemicals, it's a very light whole wheat flour because it is made from winter wheat instead of regular wheat. This flour adapts very well to recipes that call for white flour. Trader Joe's carries it, but so do Albertson's and Von's, so I imagine that if you live in the US it is readily accessible.
One other thing that I have done that is fairly simple to do is to sprout my own wheat berries and add them to bread. This of course assumes that you are making your own bread. Sprouts significantly increase the nutrient content in the grain and make the bread fairly sweet.
To learn how to sprout wheat go here.
I have made bread by just adding the sprouts to the bread recipe, it comes out with a very strong texture and a few hard bits. I prefer to dry the sprouts in the oven for a few hours on its lowest setting and then grind them in the blender before adding them to my flour.