Upon field stripping the weapon, I thoroughly clean all parts using a combination of Hoppes no.9 and Flitz polish (for the barrel). Then, I follow things up with a light coat of Weapon Shield.
For a new weapon, the main thing is to remove the packing grease and all of that junk. After you thoroughly clean it, I would suggest a quick function check. In addition, assuming this is a semi-auto, I would give the mags a quick cleaning as well...but, leave them dry inside (in terms of lube).
Regarding barrel "break in," I personally do not believe this is necessary for anything other than high-end rifles or perhaps handguns equipped with "competition" style barrels. However, I generally use only ball ammo for the first 100 rounds or so. But, this has less to do with "break in" and more to do with general (and inexpensive) test firing.