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I am new to shooting... am alooking for a 308 bolt action with muzzle break, In savage or remington my price range is about 500$.
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Welcome to LRH. There is a fountain of info here. As 4kd said use the search function. Takes a bit of getting used to but kind of opens the door to bunches of stuff.
RE: the $500 part. Keep your eyes open, stroll the gun/pawn/sporting goods stores even gun smiths. Rem or Savage are good choices. 308 is a good choice. The muzzle brake, I'm not sure of. Most rifles w/brakes reduce the recoil to about that of a 308 or so.
I don't think a brake is necessary on a 308 no matter what bullets you shoot + it adds better than a 100 bucks to the cost of the rifle. W/the 308 I feel that optics are more important than a brake. I'd put that on the back burner for awhile. I'd just as soon not use one, they don't have much of a macho factor, but on larger caliburs they make them more comfy to shoot.
Have fun and keep shootin'
I may be the slowest guy on the mountain . . . . but . . . . I'm on the mountain!