My illustrations are stored in a poly bag with a cardboard backing board and they are shipped in those storage materials in a rigid envelope that I buy from Uline.
Any other paper products I ship are shipped in poly bags to prevent damage from dampness or water. I rarely use padded envelopes, preferring rigid mailers or boxes instead. If I ever do use padded envelopes I reinforce them with cardboard inserts so they will not bend. With rigid envelopes, you must use First Class Package rates.