Out-Of-The-Box
For an out of the box BR rifle, I'd get a Cooper TRP-3. Yes, they're marketed as an "introductory" rifle, but the don't shoot like it. You'll be the limiting factor for the rifle/shooter combo for quite a while. They are competitive rifles but not the "best". Of course the "best" won't win if the shooter doesn't do his part and the best can't be purchased for $1500 or so. You'll also need a Jard trigger ($190), tuner ($150) and scope. I recommend Ron Hoehn for the tuner,and Weaver T36 scope ($400) A good rest (Sinclair if you have to have one right now or Cowan if you can wait 6-10 months), a rear bag and ammo. A cheap sport it ain't but it's lots of fun. There, I've spent over $2600 of your money and you don't even have ammo yet. Killough Shooting Sports is a great place to shop. Dan Killough is a gentleman, had good products and gives good service.
Rick