The Purpose of a New Barrel Break-In, in general, is to remove the tool marks left in the barrel. There are several manufacturing processes in which to cut the bore and then the grooves, but ALL of the methods leave tool marks.
1st, Barnes bullets are NOT recommended for barrel break-in, because the copper is too soft and won't remove the tool marks. If You choose to use factory ammo (using bullets with guilding metal jackets), You will find several "suggested methods" of the "proper" barrel break-in, and most will do the job.
On the other hand, You can either have a Gunsmith lap the bore, which is a lengthy and fairly costly process, also, after the Smith laps Your bore, he is supposed to re-crown the muzzle, adding time and cost to the work.
Or, there are bullets available (if You handload) that are impregnated with fine grit (lapping compound) that You fire through the barrel, to remove tool marks and polish the bore.
If You don't handload, the same company that offers the bullets, offers loaded ammunition using the same bullets (obviously, right).
TUBB 2000 Final Finish Bore Polishing System (bullets only or loaded ammo).
http://www.midwayusa.com/viewproduct/?productnumber=513887
http://www.midwayusa.com/viewproduct/?productnumber=847811
These are higly recommended with factory barrels....
I will also say, to clean Your bore thoroughly before ever firing a shot.
After receiving my rifle back from the 'Smith, I put the new barrel through the process. I hunt, but don't shoot a trainload of ammo, other than practice, load development, and to make sure the rifle/load/scope are still on time. That rifle will outlast ME.
NOTE: I personally have never used the "Final Finish" system, and don't think I should on my custom barrel, but should I get a factory rifle, I will use it.
"They" say that a barrel is only good for X amount of shots, but I believe that it's more so how You shoot, what kind of ammo You shoot (hot or not), X amount of shots fired in a single "sitting", how well You care for Your firearm, etc., etc...
Barrel makers say that this barrel is good for say, 3000 rounds.... What about varmint shooters? They tend to burn barrels, using small caliber/high velocity cartridges, but once Your barrel gets so hot and You continue to shoot, You're putting fire, gas pressure, and bullet material over softened steel. NOT good. What about military rifles (not a very good example)? Combat rifles, in combat, will fire MANY a Round. How fast are they officially burned out, and still maintain any level of accuracy?
There are many opinions coming Your way............