Anything reasonably priced and locally available is fine.
I have two dumptruck loads of woodchips from when the tree service did some work on our property.
I buy bags of large-flake shavings at the local feed store.
I buy bales of straw at the local feed store.
I use the lawnsweeper to rake up pine straw, fall leaves, and grass clippings from my yard. Or hand rake in the tight areas.
Now and then I rake up debris from the woods.
If ground corncob, rice hulls, or other such items *were* locally available and inexpensive I'd use them. But they aren't so I don't.
Any dry organic material is going to work -- but some need a little more management than others.
IMO, a mix of materials is better than -- and requires less management than -- one material used alone.