rbernie is correct! Let me expand:
Go to Wal*Mart (pray that they are competent in the sporting goods section)...
Order the NEF Handi-Rifle in 30-06. This comes in either stainless or blue. Stainless is like $250ish. Blue is closer to $200. If you can deal with .308, the survivor is a good choice and has a nicer pistol grip style stock made by Choate.
These will offer a decent trigger, good accuracy, and reliability. They are very robust. IMO, more heavy duty than some of these newer bolt actions.
NEF's have a very decent weaver style rail that comes with the rifle. So no need to buy expensive mounts. You will need rings though.
While there, pick a Leupold - any Leupold they have. They've got a few different ones for under $260. Clarity should be excellent, brightness good. Should be reliable. Scopes found in plastic packaging have crappy glass and are blurry. It is the only scope there with a no BS full lifetime warranty too. Leupold is famous for that. The Leupold rings at Wal*Mart are good enough. Many snobs will bash them as being junk, as they purchase rings that are $120 or more, rather than these which will be $25 or less. They will work flawlessly. Ignore the snobs. Some aren't snobs, but have other uses...like shooting at 1,000 yards or more. That's a different story.
All of this should come in under your $600 budget. You should have money left over for a box or two of premium hunting loads.
This whole package/system will give you *at the worst* a 2 moa rifle, a 4lb crisp trigger, single shot, short overall length due to nature of the action (handy, thus the name), quality optics and dependability. Of course, as with anything - test it well. 2moa is very good for any stock rifle. Ignore the idiocy on the web of people posting all their miracle groups or lying about rifle performance. Chances are, it will do better than 2 - if you're up to it.
Many will advise that you should spend as much on an optic as the rifle. That just might be the best advice. Many people spend their whole wad on the rifle, then do a cheesy scope. Bad idea. This particular option, like I said, gets you quality in both rifle and optic. Actually, really good quality in both, which for your budget listed - is very, very hard to do.