The thing I never like about newspaper (or other thin papers) is that they mat down and the worms have trouble getting to them. The corrugation in cardboard pretty much guarantees that there is no matting.
We use nearly any kind of cardboard we can find and we are not concerned with the glues. The one kind of cardboard I wouldn't use is the stuff that has colorful print on it. Diaper boxes, for example, are notoriously brightly colored and I'd never use those. Any brown cardboard is perfect.
If your city has a recycling center (nearly all do) they probably have as much brown cardboard as you could want. This is where we get most of our cardboard!
