I package my ground by loading it is the sausage stuffer, and stuffing the commercial bags. I twist them up carefully so as not to trap any air inside, and seal with a 3/8" hog ring. Having a dedicated stuffer is the only way I have ever done it. The more times your meat sees the grinder, the more chances of the the proteins getting heated up, and changing flavor.

Lots of good info here, I don't disagree with anything mentioned so far.