Boyd is 100% right. Build a 6PPC to 10.5lb and you can compete in sporter, LV & HV. You can also compete in Unlimited, so that lets you shoot virtually all forms of registered BR matches. For stocks, I really like the Scarborough and Leonard stocks, but you may not want to wait as long or spend as much as you will need to, to get one of these. A lower cost and probably more readily available alternative would be the Robertson stocks sold by Stiller or Borden. For a barrel, I like Bartlein or Kreiger. A 4 groove, 1/14†twist is probably the best start, but there are a lot of twist options and it will depend on the bullets you use.
Find a good gunsmith. By “goodâ€, I mean someone who can make winning BR rifles. Do NOT have the rifle made by someone who has not built a BR rifle before. There are many other details to consider beyond the points I have mentioned above, and a good gun smith can help you decide on some of these. I have personally used, and have no problem recommending Wayne Campbell and Clay Spencer. These guys are both current competitors, first rate smiths, and will steer you in the right direction. Other guys like Dwight Scott, Billy Stevens and Gary Ocock are all very highly regarded and have excellent track records, and there are many others out there.
Lastly, you dont mention if you are going to matches much? Once you work out your build, you really should get to as many matches as possible, and particularly talk to experienced, high level shooters. Someone will probably help you a lot in getting to the next level in loading, shooting technique, etc.