I am a mauser style controlled feed rifle fan. With that bias in mind, here are links to my recommendations:
CZ-USA -> CZ 550 American
The CZ is an excellent rifle, with features and quality that cannot be found on any other rifle in its price range. If you can live with a wood stock, here is a screaming deal on a CZ 550 in 30-06:
CZ 550 American 30-06 : Bolt Action Rifles at GunBroker.com
I am in love with the new production Winchester Model 70's. I have a standard sporter in .264WM. I am not a big fan of their synthetic stocks, though. YMMV.
Model 70 Ultimate Shadow, Bolt Action Deer Elk Big Game Rifle -- Winchester Repeating Arms -- Product Model
These can be had pretty reasonably. Here is an example:
Winchester Model 70 30-06 Ultimate Shadow 24" : Bolt Action Rifles at GunBroker.com
The Zastava M70 (actually a commercial Mark X mauser sporter) is, IMO, about the best deal going. It's also one of the least well known options out there. I have several rifles on this action.
Century International Arms
These rifles can be had for not much more than most domestic manufacturers' budget rifle. Here is an example:
98 Mauser,Commercial Mauser,Walnut,30-06 : Bolt Action Rifles at GunBroker.com
If you shop carefully and bid carefully, this rifle can be had for under $500. If you can't live with the wood stock, $250 buys you a Bell & Carlson fiberglass stock with aluminum bedding block in the color of your choice.
Any of the above rifles are quality arms that will shoot accurately right out of the box. When you get your rifle, test it with match grade ammo first to see what its potential is with factory ammo. Then test regular hunting ammo until you find a load that you are satisfied with.
With an off-the-shelf rifle shooting off-the-shelf ammo, you will run into practical limitations that will most likely prevent you from hunting at long range with it. With some practice, however, you should be good out to 4-500 yards. If you handload and tweak your rifle a bit, you should be able to extend that by a fair amount.
A standard sporter should serve you well in this role. For what you are going to ask of your rifle, you don't really need a heavy barrel.
There are cheaper rifles out there than the ones I have recommended. The above rifles, however, represent what I consider to be real value for the money. I believe that they are good examples of a balance between quality and cost.