I once had a 6BR and liked it, but had it rebarreled when I tired of it. For an all-around target cartridge it is great since it has a greater capacity than the 6PPC and can give .22-250 performance with 55-grain Noslers on varmints. It has a very high accuracy potential, although the 6PPC will shade it in top-level BR competition. That was fine with me, aggs in the 0.3 moa range were fine with me. That's four, 5-shot groups averaging in the 0.3s, not just one bragging group.....
Done right it won't be cheap. I like Hart barrels, although I've used Lilja and Jarrett with excellent results. You can go the route of custom dies - done right they work the brass very little and cases last forever. I assume the 'smith will true up the receiver and use a thicker recoil lug when he puts on the barrel. He should square up the bolt face and lap the bolt lugs to even contact as well. Trigger is up to you, but a factory trigger will limit your practical accuracy with the rifle.
Stock - make certain that the action is at least pillar bedded into a good 'glass stock. A glue-in is "better" by a tiny amount, but you need a large freezer to remove the action. My most accurate firearm was glued in, but a good pillar bedding job is almost as good.
Barrel care and shooter technique will have a great effect on the rifle's performance. After it's built it's all up to you!