I use the Tipton brand rod for my .270 win and my 7mm rem mag, and with those I use a nylon brush, unless they are terribly cruddy then I use a bronze.
As far as solvents go, I have tried about umteen different bore solvents, You name it I have probably tried them,, I like the Bore Tech Eliminator, for my copper fouling,,, as far as carbon goes, it does a decent job on that also.
I use only one type of "gun oil" and that's G-96, its heads and tails better than anything else I've tried since I was a kid cleaning my first .22 rifle. I use to get Tri-Flow, it's similar to "Break-Free", but has a better residual oil film I think, but by far the G-96 wins hands down. (and smells like bubble gum)
You should use a bore guide also, and I use the Tipton brand but its not quite the very best, it actually could have been designed better.