my vote, (the more expensive option) is a Remington 700 Sendero chambered in ether 7mm Rem Mag. .300 Win Mag or one of the RUMs it is offered in (7mm or .300)
The Sendero is essentially a more accurate 700 with a fluted stainless 26" heavy barrel, an extremely nice gun, and even though Tang is a Ruger man, I'm fairly sure he has nothing bad to say about the quality or accuracy of the Sendero he used to own

If your experianced then this is probably the way to go.But it gets you over your budget as the rifle alone cost more than your willing to pay . Then you also need a good scope to go along with that rifle .
In fact you really need two guns . you could hunt with a Savage Edge or a Marlin Bolt action in 308 W to 3006 which would cost about 400 dollars depending where you shop , and these guns would suit to hunt .But they would not be something for a day at the gun club on the range .
How ever to target shoot , you need a rifle that weighs a bit more, a longer and heavier barrel ,a good scope for target use, as the cross hairs would be too thick on a hunting scope, then for target a hunting scope the cross hairs would be too fine and too much power to hunt with . Then a different stock than a hunting rifle and so on .A rifle suited for the range then is going to be too heavy and awkward for hunting.
So again you should go to the range and see what is being used and note what calipier . then decide what you want to buy first . A target rifle , or a hunting rifle .
So in respect to say it differently, you want to do two jobs . For one you need a good solid truck, and the other you just need a car.