If you are wanting to hunt med. size game (whitetail, mule deer antelope etc.) then id buy either a Savage 11/111 hunter xp in .270 win or a .308 or a remington 700 sps in .270 or .308 both under $600 with a scope, both good guns and the .270 will let you take anything from coyotes to elk (with the right bullet and shot placement).
The scopes that come on these rifles arent great, but they will do for a year or 2 until you can afford to buy a bit better of a scope.
http://www.cabelas.ca/product/34257/remington-700-sps-dm-bolt-action-rifle-w-scope-hard-case
Savage 11/111 Hunter Xp
http://www.cabelas.ca/product/36742/savage-11111-hunter-xp-bolt-action-rifle-w-scope
Savage 11/111 Trophy Hunter Xp (better scope i believe then the hunter xp and has the accu-trigger which is awesome!!)
http://www.cabelas.ca/product/36750/savage-11111-trophy-hunter-xp-bolt-action-rifle-w-scope
I prefer a .270 for a couple reasons, not saying a .308 isnt a good caliber, my buddy shoots .308 and loves it, im a .270 guy for a couple reasons
1) Flatter shooting: you dont have to compensate for drop as much as a .308, although under 350 yards they are the about the same.
2)Ammo is everywhere, no matter where you go someone will have .270 ammo. They will .308 too, but maybe not as many options
3)depending on shooter and rifle, i find .270 has less recoil cause of the lighter bullet then a .308.
But finally its all personal preference, the animal you shoot wont know a difference when its dead, and pick what gun fits you, then pick your calibre, you wont shoot accurate if your gun doesnt fit you. .308 and 270 are both awesome calibers that do the same thing, its personal preference.
Good luck and happy hunting!