If your new barrel is a match quality handlapped barrel, the only part of it that will break in with shooting is where the reamer cut the throat.
I agree there is a lot of debate and theory about breaking in procedures and if any breaking in procedure is beneficial or not.
Some barrel makers recommend a procedure, others do not. No one can say for sure if you should or should not break in your barrel.
For what it is worth here is a procedure I have used. The word "clean" refers to a barrel that has no powder fouling and no copper fouling.
When cleaning, always use a good bore guide and a good rod.
Start with a "clean", lightly lubed barrel, fire one shot, then run a loose patch through with Sweets 7.62 or any other solvent that will “eat” jacket fouling. Saturate the bore and let it sit a few minutes. Sweets indicate jacket fouling with a blue colour.
Run patches through to dry the bore and then wet patch it again and saturate the bore. After a few minutes dry patch it again. Repeat until the jacket fouling is removed (no blue patches).
After cleaning with Sweets, brush with Hoppes #9 and dry patch the bore and then leave it slightly lubed with a wet patch of Hoppes #9 before firing.
Then fire one more shot, and repeat the above procedure. Do this for a total of 10 shots, and then proceed to fire 2 shots and then clean as above, for 10 more shots. (For a total of 20.) The barrel is now broken in. It should be cleaned after every 20 or 30 shots there after, if possible.
You will find when the bore is broken in properly; the cleaning procedure is very quick, because there is very little jacket fouling in the bore.
I prefer Sweets 7.62, because it shows “blue” if there is any jacket fouling. I never use a copper or bronze brush with Sweets, because it will eat them, and give a false blue indication of fouling. I never let any other chemicals mix with Sweets. That is why there is a lot of dry patching and swabbing with rubbing alcohol and dry patching between switching chemicals.
For storage after cleaning with Sweets, dry patch and then swab the bore with several patches using rubbing alcohol; this will dissolve any remaining ammonia. Then lightly oil the bore.
Ammonia based cleaners will not harm a rifle barrel. They will leave it so clean though, that the bore will be susceptible to rusting. Ammonia based cleaners should not be mixed with other chemicals as unknown reactions may occur.