Cost to ship 1lb in a paper tube vs plastic bag

I will be a new seller and initially fulfill orders myself and then will have Amazon fulfill. I have an eco friendly brand and am considering to ship my 1lb product in a paper tube 2.5” diameter x 6.6” height.

I’m wondering if packing in plastic bag causes shipping cost to decrease and by how much. Is there a good way to estimate the cost of shipping and whether Amazon would fulfill using a cardboard box or flexible plastic mailer.