USPS has been my carrier for the last several years, without problems. Most packages arrive within a week during normal times of the year.
Most artwork is covered with glassine or placed inside a clear bag to protect the surface. Then shipped flat, sandwiched between foam-core boards, and taped all-the-way around.
Some artwork, such as large canvases or prints, may be rolled with glassine and shipped in a tube. This saves space and better protects large artworks and frames from being bent, punctured, or crushed.