Brian, there's lots of GOOD discussion going on here, and personally, I'm glad it is.
Used to be, the BR shooters used Hart, Shilen and later McMillan barrels. A long time ago, Douglas barrels were popular. Looking at range reports from a couple of local shoots (Dunham's Bay, NY and St Johnsbury, VT), I see Krieger and Lilja barrels mentioned a lot more than they were 15 years ago. I'm a Hart fan myself, but, that's almost as much due to knowing the original Hart's (Bob and Paul) as well as Bob's son, Wally, as it is because of the quality. A guy named Niemi used to make barrels for himself, then later for others. They made Hart barrels pale in comparison.
I also concur that 30 caliber is a good start point. It's real easy to make a 308 shoot well, and they're better in the wind than a 223. 300 Mag's leave some to be desired, and though they certainly can cause flinching. Someone mentioned 6.5x284. I politley disagree, and here's why. The only calibers that have good custom bullets available are 22, 6mm and 30. Mass produced bullets like Sierra, Hornady and a few others are OK, but, if you've ever used the custom bullets, man, what a difference. The mass produced bullets are capable of 1/4 to 3/8 MOA, but, the custom bullets can get you down under 1/8 MOA. BTDT, and it's nice to do.
Just for the record here, I do my own gunsmithing, including truing actions, fitting, chambering and turning barrels (I buy straight blanks), and my work is pretty decent, based on the results I've gotten in the past. I can say I know WHY the 'smiths prefer to work on the Remingtons, they're easy to do, and are pretty close to right to start with. Custom actions like the Hart and such don't need to be reworked, they're made right the first time. They do cost some serious $, though.