Hiya.
I use newspaper in the hutch or shed with litter trays with Megazorb and loads of hay.
Megazorb is brilliant in my opinion because it's kiln dried wood pulp so it's very absorbent and you don't need much, making it very cheap overall. Not only that, because it's so absorbent, it doesn't smell even if you bunny has used it quite a lot! You can compost it afterwards or even dig it straight into your garden. As it's kiln dried, it's very low dust and all of mine seem to like it a lot.
I buy it from a local farm shop but you can get it over the internet too. If you can't get that, I can also recommend Care Fresh of even Bio Catolet. Both safe, absorbent and you don't need much.
Personally, I would never recommend shavings as I have read quite a bit about how it can harm bunnies. Firstly it can be dusty. When a rabbit wees on it, it releases phenols which are thought to burn skin and is also thought to have an effect on the respiratory system.
One bunny I re-homed from a woman on Freecycle had kept the bunnies on wood shavings. They weren't neutered. Despite having pre-ops and otherwise being in good health, on the day of the neuters, the boy bunny didn't make it through the anaesthetic. My very bunny savvy vet did a necropsy and found his lungs to be full of dust, likely to have been as a result of being kept on shavings.
Just my experience but I would rather never take the chance again and will stick with Megazorb.
I'd be interested to hear other bunny mummy and daddy's views on shavings.