I didn't have to perform any of the shipping (or wrapping duties) on this occasion, but the USPS has become the default option of most of the folks I know that are still doing it. UPS can be a pain at times, depending on the vendor you use. While nothing is cheap to ship anymore, the Post Office is still the least expensive option. Collecting on any insurance claim can be a nightmare, so...try to avoid that. I ship only on Mondays to eliminate having it hanging around over a weekend somewhere (always seems to lead to trouble).
Nobody ever asks what it is you're shipping (you have to make a few declarations while paying for and insuring it all). Doing a very good job of packing is critical these days (see above, right?)