You don't have to use fleece, that is just what some people use, I think mainly because it is less expensive than buying so much bedding all the time because some of the cages people have are so big. I use the recycled paper pellet bedding, I don't want to have to worry about cleaning fleece all the time or the smell. It is up to you, just don't use cedar, of course. And hay is for them to eat, not to use as bedding.
Oh, and they should have access to hay ALL THE TIME, not just as a treat. Hay is very important for their digestive systems and teeth. I have a hay "hopper" on the outside of the cage so I can put hay in there and it will poke through the cage bars. Hope this helps!