The intended purpose of the rifle has a lot to do with which one to select. Also, there is the question of handloading ammo versus factory ammo.
If you put some geographic info into your profile we would know generally what part of the solar system you live in and not have to ask whether you are hunting eastern whitetails deer or Klingons. Any cheap laser gun is good enough for hunting Klingons.
Shooting at 600 yards leads to shooting at 1000 yards which leads to busting rocks at distances which you wouldn't believe. Depending on geography, you may never need a gun and scope that is capable of shooting past 1K. Also if the gun must be used to hunt whitelails in the swamps of Gerogia at 30 yards then it starts to limit barrel length and scope power.
If the gun is simply a paper puncher, then one of the new competition Savages and a good quality fixed power scope will get you under the price cap and there is plenty of factory match quality ammo in 308 if you do not handlaod. I have heard rumors that people actually use a 308 for hunting also, even though it does not have the word "magnum" in its name. /ubbthreads/images/graemlins/grin.gif
A little more information will help with the answers.
By being very careful with costs, you might could squeeze out a custom gun for that price, certainly you could pick up a used one if you were willing to take a chance with somebody else's gun or knew the person was honest. The 40X I was shooting yesterday was a used very little gun and would have met your cost window if I had accepted the scope that was offered with the rifle and not put on a super expensive scope.
I put away my long range rifle for nearly 25 years before coming back to the sport and I am just having a great time fooling around with rifles and shooting just about anything that my crosshairs settle on and sometimes my crosshairs don't settle so I just make a lot of racket and call it a good day. /ubbthreads/images/graemlins/grin.gif
Anyway, welcome to our galaxy no matter where you are from.