Go to Krieger barrels or even Shilen like their FAQ http://www.shilen.com/faq.html#question10
Personally with a new barrel I follow the cleaning regimen clean after each shot for the 1st 5 shots, then clean every 5 rounds for the next 10 strings. I check for copper fouling after I've fired the first 10 rounds, and then check for copper again after the next 20. If it looks good after that- I shoot until it shows me signs it needs attention, or I put it away for storage.
I focus on keeping my action area clean and the outside of the gun is properly tended to.
In a humid environment like it was in WV- I cleaned and oiled my barrels more frequently due to conditions. But in Montana I just don't need to worry so much about it.
You will see a lot of opinions on the matter, and that's okay. Honestly I would never disagree on the subject. I tend to follow a regimen for break in and let the actual conditions of the barrel and the shot accuracy dictate what to do.
I did shoot one then clean for 5 rounds in a row, then I shot a string of 5, cleaned, shot one then cleaned for 5 rounds, then shot a 5 round string and cleaned and called it good. Then I did my 20 rounds of load development without cleaning and then cleaned after. Would you do any more break in after what I did, or would you call it good?