We use all kinds of different things for coop bedding and nest bedding. There is no one thing that is “best” for all of us. Depending on what the coop or nest looks like or how we manage them there might be something better for that specific situation but lots of different things work great for both.
The hens will be able to tell the difference in the nest and the floor. You can use the same thing if you wish or something different. It’s not the bedding that makes the nest, but it looking like a good place to lay. Hopefully that will be your nests but it could easily be some place on the floor or somewhere else that looks good. It could be a corner, under your nests, or even just a place shadows make it look “hidden”. Fake eggs like golf balls, wooden or ceramic eggs, even plastic Easter eggs help.
For the coop floor some standard bedding materials are sand, dirt, wood shavings, wood chips, straw, hay, grass clippings, or dried leaves. For nests some standards are wood shavings, straw, hay, grass clippings, carpet, rags, and Spanish moss. One guy folds chicken feed bags and uses those. I cut tall grass stems, dry them, and use those in my nests. I guess technically that could be called hay. It’s free for a little labor.
A standard problem when the chickens are scratching out the bedding in the nest is that the nest does not have a high enough lip on it to hold the bedding in. When they are getting ready to lay many hens scratch around to arrange the bedding just right. If the lip is not high enough the bedding, fake eggs, or real eggs can be scratched out.