Well, for bedding, what i typically do is go to walmart and get some cheap compost. Its usually like 3 bucks a bag. Ive never used cardboard or newspaper. They seem to like it. And then when i take some out of the bin to put into a pot. I dont have to worry about separating anything, cause its just all mixed into the compost.
I put EVERYTHING into my bin, minus oils, meats, or fat. I even put flat beer in there, and they love it.