Whilst most goods sent are unpacked within a short time frame, I think acid free paper is the way to go to prevent leaching as Amber notes as well as prevent tarnishing of silver or dulling of other goods. 

A thicker tissue paper is not necessarily always the best choice. It depends on the type of item you are packing.  For example, for finer silks or items with delicate bead work, soft thin acid free tissue paper is usually recommended.