It is probably too bad that you have asked this question as your debut on the board. It will generate opinions all over the board, perhaps even some strongly worded ones (based on past go arounds on this issue.) So rather than getting a clear consensus, you may come away thinking that we don't know what we are talking about, and not only that, are kinda mean about it.
Some people will tell you that you can go out and shoot it just as hard as you want, right from the start. Others use a far more intricate and time consuming shoot/clean/shoot/clean regimen for the first 20-50 shots.
The problem is that no one really knows for sure--no one has done the kind of controlled measurement over a large enough sample to know definitively.
My approach, for what it is worth, has changed a lot over the past few years. First, if this is a new barrel, I would clean it really well to make sure there is no fouling from any proof shots at the factory. Then I would coat it with Ultra Bore Coat, following the directions carefully. I have used that product on some barrels recently, and think that it has a far bigger positive effect than the old painstaking break in procedures I used. Barrels I have put it in foul much less and require less cleaning than my experience would expect, and that includes big magnums that should be prone to copper fouling (like your 300 mag).
Welcome aboard.
