I think Aubiose is chopped up straw or hemp, its great because it absorbs the damp and smells and is still quite dry and 'fluffy' where as paper will soak up damp but be wet. If you do use shredded paper make it cross cut rather than strips as they can wind around legs.
Aubiose sells for somewhere between £7 and £9 a bale normally
Hemcore is another alternative and is slightly cheaper and coarser
Easibed is another brand name but I dont know which of the two above it is more like
All of these also compost very quickly which is a bonus!
Woodshavings (dust extracted) are good but take longer to compost
I use Aubiose in the nest box and pull out tray and use woodchips and Aubiose mixed for the run
A shower curtain over the Eglu run is a good idea as it will keep everything dryer! Never use Aubiose in an uncovered run as its like a sponge! IKEA do cheap clear shower curtains, I have used a clear tarpaulin from Tarpoflex. Corrugated sheets of clear plastic from Wickes/B&Q also work - attach with some bungees
My run and cover is shown below (you don't need a blanket over your Eglu - I am just paranoid!)