I'll just focus on the noun, and add that in the UK you'd probably just say "some meat" or "<some weight of> <specific meat>" (e.g. "a pound of brisket"). In the UK, food comes in "packets" rather than "packages". In the US, it's the opposite. So in the US you might well say "a package of meat".
In both countries a "pack" can also mean something you carry on your back (backpack). In both countries, as others have already said, you put "packages" in the mail/post (but there the word means something wrapped and taped up, not a container of food).