Making whole wheat bread in a bread machine? What kind of flour? Disclaimer: I may not know what I'm talking about, feel free to correct me if you think I'm making a fundamental error.

I just got a bread machine and I love it.  It's so easy!  But I'm experimenting.

The first time we used it, we used a store brand white all-purpose flour, and the bread simply wasn't very good.  It was crumbly, it collapsed a little in the bread machine, etc.  I mean, it wasn't bad, we ate it.  But I wanted better.

After that, we bought King Arther white bread flour, and it worked much much better.  The bread was delicious with a wonderful texture.  I don't know how much of this is because it's bread flour (I assume mostly this) and how much is because it's a nicer brand (I assume this is a smaller factor).  It's great bread!

However, I'm told that white bread in general is not as healthy as whole wheat bread, although I'm not exactly sure what whole wheat means or how much healthier it really is.  Therefore I want to make "whole wheat bread," whatever that means, in the interest of health.  And to be honest, I've had some very boring whole wheat bread, and some incredibly delicious whole wheat bread.  It varies.

So, what do I need to do?  I assume it's a question of getting the right flour, but I didn't see "whole wheat bread flour" in my store- is this because it doesn't exist, or because my store doesn't carry it?  What should I be looking for?

Any tips, specific or vague, would be appreciated.  Thanks mmuch.
Bread flour has more gluten, which is a protein that makes bread stretchy and less crumbly when the dough is prepared right. There is plenty of whole wheat bread flour out there, and you can often get mixes which are specifically made for bread machines, I'd start with those and see how you go. If you cannot find them in your local store you might be able to find them online. 

You can also read the label on the back of the flour, higher protein flours generally mean they have more gluten. You can sometimes find non-bread flours that have almost as much protein as those marketed as bread flours, so next time you are at the store have a look.