Here are my top Four;
1. Krieger
2. Hart
3. Lilja
4. Shilen
IMO, I think Kriegers are the best, however, the other 3 are awesome too. Any of the top four are awesome barrels, so you can't go wrong with any of them. I've had really good results with Krieger. I've also had good results with Liljas too. However, the Kriegers just seem to work best for me.
There are other barrels out there I did not even mention. Such as Lawton, Broughton, Spencer, Bartlein, Pac-Nor, just to name a few.
Talk to your gunsmith, and I am sure he will give you his advice on which barrel he likes. Also, look on the Benchrest and 1000 yard Benchhrest sites to see what those guys are saying and see what type of equipment their using and winning with.
I think many on this site either use Krieger or Lilja. If I were you, I would go with a Krieger. Good luck with your choose. Keep us informed.
Also, can you give us some info on your build. What caliber, Action, Stock, and Trigger will you be using.
Wildcat