[Jack]

Oh Boy!
The 'new barrel break in' is one of those things where everyone has their own way of doing it, and no one has real proof that their way is more effective than others.
Proper cleaning is somewhat that way, too- everyone's got a regimen they believe in.
I think I can safely say that, for proper cleaning, you should always clean from the breech, if possible, always use a bore guide, and always use a 1 piece cleaning rod. Some prefer coated rods, some plain steel. Either way, getting in the habit of wiping the rod down with a cloth frequently to remove bits of grit before they can get in your bore is a wise precaution.
The new foam bore cleaners seem to be favored by a lot of people. Bore solvents is another one where everyone has a preference, and there are a lot of good ones on the market.
Then there's bore brushes. Some favor no brushes, some like nylon, some think you need to use bronze brushes.