There seem to be many that are capable of precision, which is what I think you really mean, but for you to shoot accurately you need to consider the package as a whole: rifle, scope, mounts, ammo. Start with a rifle that fits you and feels good to you in operation, then add the other stuff, paying special attention to acquiring a reliable scope and sturdy mounts. Without a solid optics setup, you’ll be unable to take advantage of the precision that modern manufacturing allows at even bargain prices.
For quality at bargain prices, I always start with Howa or Weatherby Vanguard. Many like Tikkas, and there are some inexpensive rifles from Mauser, Sauer, and Franchi that are reportedly “accurate”. Lots of people buy RARS too. A kimber Hunter, if you can find one, is worth a hard look. My son has used one for several years and likes it a lot. I considered one in .308 last year, but ended up with an M70.
