I'd pick the small children, much more readily available, not to mention they are very absorbant.
Just kidding of course!
I keep all of mine on newspaper(it is printed with soy/vegetable inks, so no harm to anything really), and the two corns, who have found homes, are kept on a bit of aspen(they like to burrow in it).
Bed-A-Beast is fine as long as it is cleaned out regularly when there is a bowel movement or they urinate.
I've used cypress mulch from Home Depot as well, and it works just fine. Same as above though, needs to be cleaned regularly. I usually baked it as it always came wet. I think a HUGE bag of the stuff was around $3.
Aspen is good too, but if it gets wet it needs to be changed. Mold happens pretty readily with it.
And you're definitely right about the carpet, it tends to get gross very quickly. Think about a kitchen sponge, how it starts to smell nasty even if you wash it in bleach. The carpet also can rough up their belly scales and make them ragged.
Anywho! Hope that helped!