I happen to like Burris Signature Zee rings. That's what I use.
As far as barrel break in, do a search for that term or related terms and you will find any and every technique imaginable described, argued and analyzed in painful detail.
Although many people have "success" with lots of different methods, interestingly enough, no one can define what a barrel break-in "failure" is, so to me, it sounds like it is all really guesswork.
My suggestion is to not worry about it too much. Do a bunch of reading about it, pick a methodology that makes sense to you and go for it. Since you are putting together what is primarily a hunting rifle, you will likely not wear out your barrel even after the rifle gets passed down through several generations of hunters.
That's my free opinion. Worth at least double what you paid for it.
Edit: Oh, yes. I almost forgot. Welcome to the forum, we're glad to have you here!
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