It is soft and dust-free, but it can mold quickly when it becomes wet. Carefresh is made of wood pulp by-products from the pulp and paper industry used in the manufacture of paper and cardboard. They don't use dye nor chemicals, and it's virtually dust-free.
Don't even consider cedar. The fragrant oils (phenols) are toxic and can cause respiratory damage to your piggy. Pine, especially, is often debated because it contains fragrant oils in its natural state, but oven/kiln-dried pine is available.
Both are popular as burrowing material, but remember that they can mold rather quickly. A soft pile of hay makes a great burrowing spot for your cavy. But beware of sharp ends that can poke your cavy in the eye. If you want to use straw and hay, use it as a top layer with some newspaper or other bedding below it. Make sure that it's not moldy to begin with, and break up long, hard bits of straw that can be sharp.