Most of my sales are small, 8x10 or smaller and usually done on panels. I ship them in flat rate Priority Mail padded envelopes. These are great because the post office will deliver them and a lot of other mailing boxes and supplies right to your door for free.
First thing I do is wrap the painting in glassine paper to protect the surface of the painting. Then I sandwich the painting between two 9x12 cardboard pads. These pads will fit nicely into the envelope and they can be purchased on Ebay quite cheaply. Then I just drop the envelope off at the post office.
Larger paintings than that get wrapped in brown craft paper, then wrapped in bubble wrap and placed in a box that allows for at least one inch of free space all the way around the painting, which is filled with newspaper. Those boxes I will buy from websites like Uline.com.
I’ve never had one complaint about a damaged painting that I’ve sent out.