I use fleece blankets on the bottom of my bun's cage. I bought a few yards from a fabric shop and cut them into pieces that fit the bottom of the cage (I got 3 pieces per yard). My bun doesn't pee on them, so I just remove them once per week (or sometimes a bit longer if they still seem clean), sweep up, and replace with a new blanket. I just wash them in my washing machine - very easy and reusable.
Towels can also be used, but if your bun chews them they can get strings that can mess with their digestion. Fleece is recommended because if they chew it it's not dangerous.
If your bun is not litter trained, you might want to start with a bare cage floor - sometimes buns will pee on anything absorbant, so this could hinder litter training if he's peeing on the blanket. However, when I brought my bun home he wouldn't walk on the bare cage floor, so I had to put down fleece immediately. He picked up litter training right away though and never peed on his blanket.
I currently use Yesterday's News in his litter box, but I have a bag of wood stove pellets I'm waiting to try out. I also put a lot of hay down so that he'll eat hay and poo at the same time. I clean his litter box twice a week and I don't notice any smell, but some people clean more often. A 50/50 vinegar/water solution can be used to clean the box and any pee in his cage.