First, invest in some good equipment. A one piece coated cleaning rod should be the first thing on your shopping list. I like Bore-Tech the best, but Dewey makes a good rod too. A bore guide is a must too. Here, I prefer Sinclair, but I think Stoney Point makes a good one too. Also, get a brass jag and cotton flannel patches. The synthetic patches and the ones made from t-shirt material don't work nearly as well as 100% cotton flannel.
As far as brushes are concerned, well, the stainless steel variety is certainly a no-no, but bronze brushes will absolutely NOT harm your bore. Practically every custom barrel maker recommends them. I've been using them forever and never experienced any barrel damage as a result. I've got a rifle that's over 80 years old and has had a bronze brush run though the bore thousands of times and it still shoots just fine.
There are many good solvents out there today and I've used just about every one at one time or another. I've pretty much settled on a routine of using Shooter's Choice for powder fouling and and then following that up with Barnes CR-10 or Wipe-Out for copper fouling. I follow these up with a good bore oil. Presently I'm using Butch's, but Rem oil would work as well.
A squeeky clean barrel isn't a must, but definitely make sure there are no obstructions in the barrel prior to shooting. Swab out any excess oil in the bore. About two weeks ago a friend of mine screwed up his brand new rifle because there was some sort of obstruction in the bore when he first shot it. My guess is that it was excess oil. Anyway, whatever it was, he put a nice donut shaped bulge in the barrel about 6 inches from the muzzle.
One last thing, just go out and shoot the rifle, enjoy it and clean it after every 20 - 25 rounds or so. Don't worry about this break-in nonsense. Just don't let your barrel get too hot. I shoot 3 shot groups then let my barrel cool back down before shooting another group. In hot weather a damp rag placed over the barrel between groups will greatly speed up the cooling process.
Good luck, enjoy your new rifle.
