I suggest using whatever you have available and/or what ever is the least expensive. In my case, I use straw that I get off my land. I have a 2 acre field of course grass and tall weeds that I bush hog with our Kubota tractor. I hand rake it and then haul the straw on a tarp which I pile up under a covered but open area of my barn. I use this straw to cover the floor of my 9 x 14 foot coop and when it gets soiled or damp, I put it in the compost pile and put down fresh straw. I also use this straw in my nest boxes. The hens seem to like it just fine.
It's free and just takes me a bit of sweat equity to gather. Because my coop is rather large, I don't want to have to pay someone for either wood chips or straw or hay or any of that. This would add up in expense rather quickly, I would think.
In the nest boxes, the hens never kick any of the straw out. Nor do they eat it. They have never kicked out any of the 6 fake easter eggs or real eggs out of the nest boxes either. I made my nest boxes out of a big plastic drum barrel I had on hand. I cut the barrel in half across the middle and used each end as a nest box. I put a black rounded top type garbage can lid on the top of each nest box to keep the chickens from climbing on them. The lip on the front of each nest box is about 6 inches deep, measuring from the lip to the bottom. The opening itself is 10 inches high by about 14 inches wide. I face the entrance to each nest box away from the light so it's relatively dark inside the nest box and with the black lid, it's pretty perfect for the chickens.
I also free range (no run, no fence, secure coop at night) and despite the infinite options for where the chickens could lay their eggs (in the forest, in the huge straw pile, under the tractor, in the dark corner of the barn, etc etc, etc!) they ALL lay in the nest boxes. So, despite the home made design, these boxes seem to work for the chickens. Also, because I free range, I spent time upfront trying to show my hens and my rooster that they were to lay the eggs in the nest boxes. Here are 2 threads on this:
https://www.backyardchickens.com/t/837728/rooster-doing-a-jiggy-dance-for-the-hen
https://www.backyardchickens.com/t/837586/newbie-waiting-for-eggs
So.... all this said, I'd suggest going with whatever nesting material you have either on hand or that is easiest and least expensive to get. I honestly don't think the chickens mind all that much either way. What they seem to care most about is if the nest box is in what THEY perceive to be a quiet, dark, safe place to lay their eggs.
Maybe more info that you were wanting but in any case, hope this helps!
Guppy