I use waterproof crib pads for mine...they're sturdy, you can bleach the heck out of them, and though most of mine are fuzzy, the fuzz does not seem to attract them as far as picking at it. I prefer the crib pads that feel more like thin, heavy felt, no fuzz on those, but I only have two and haven't been able to find more like them... I also use quilted cloth incontinence pads like they use in hospitals and nursing homes. We use those for lining the whelping box for litters of puppies, too. I borrow them when I have new chicks and they work well. Same as with towels, though, you really need to check them for loose threads, tags, etc. But they work great.
Can't wait until I can switch over to shavings!!! Good luck with your babies!