Any absorbent softwood shavings are fine, I use SNOWFLAKES brand which is light and absorbant. Some shavings can be thicker and less absorbant like chips really so avoid these if you use shavings. I've also used mixed shavings with chopped straw which is good for bulk and useful in the nestboxes and cheaper but less absorbent. We've used Hemcore for the horses and the recommended way is to use a very thick bed and poo pick regularly. I've not used it for chx though it clearly works for many people on this site so might try it too as it composes well I believe.
Hay, as Grumpydad says, contains a lot of nutrients as the seed heads are included where as straw is much more sterile being just the stalks after the grain is extracted. This why hay can be very dusty and is much more likely to go mouldy than straw though any bedding can produce mould if not kept dry and managed properly. Being very palatable hay is liable to be eaten. I've heard this can cause crop binding though not seen this personally. However it's not a good idea to encourage litter to be eaten for obvious reasons so hay is usually not recommended.
I wasn't sure but it sounded like those who used shredded paper were talking about it's use as nesting bedding which is different from using it as a floor litter where it's obviously going to get exposed to much greater soiling. I would have thought Dizzy lizzie's experience was nearer the mark on the use of paper.
I believe there's a company who use reclaimed softwood to produce bedding (also used for large animal bedding and recently extended to poultry) which is obviously good from a recycling perspective but I'm a bit dubious that there seems little rigorous control on what gets shredded as it depends on a manual sort process and it wsould appear impossible to guarentee to weed out any potentially toxic scrap wood which for instance might have been treated for woodworm etc. So I stick to clean softwood specifically produced for shredding or shredded scrap offcuts.
HF