When mailing a handful of coins first I 1.
vacuum seal coins in a bag, already measured for the envelope to be used - using a FoodSaver machine, this way the coins don't jingle or move around while in transit. 2.
fitted in a bubbled padded envelope or box (depending on the weight) - not too lager or too small for the sealed bag. I prefer the Poly Bubble envelopes because they are tear resistant and waterproof, especially when mailing out of the US.
There has been times I have received coins and other things in one of those padded yellow/brown envelopes and found holes or cuts and was sure glad the contents were intact. But to play it safe I go with the Poly Bubble Mailers.
When mailing one or two coins I put them in a flip or 2x2 if available or vacuum seal them long enough to fit in a #10 envelope.
I have collected from the PO those Priority Mail envelopes and cut them up to the size of the envelope I'm going to use as a "padded" protection.
For banknotes I do the same. If I don't have sleeves I put them in reg envelope and cut up those Priority Mail envelopes to the size of the envelope being used then put those in the addressed envelope. Just as I did for the prizes I just mailed out Wed. So they were well protected.