I like to use paper lunch sacks over deli cups and cloth sacks.
For big lizards I use grocery bags or the heavy paper bags used for taking ice cream cartons home from the grocery store.
The deli cups are hard- when the box gets jarred I imagine a head hitting the side or lid of the deli cup. The cloth bags are abrasive. Especially when dampened slightly. Paper bags are soft (compared to deli cups), and non-abrasive (compared to cloth bags). They can be taped into the shipping box so they do not move at all during transit, leaving more room for air in the shipping container.