You can get a great rifle for that price. My suggestion would be the Savage Model 10 or 110 depending on if you want a caliber that's in a long action or short action. They run between $387 and 397 at Walmart depending on which one you go to. They have the famous accu trigger and even come with a Simmons scope as well as a sling. It's just a great all around rifle. The scopes serviceable, but not the best, but it should work fine. It's really a great gun, and that would leave you $100 left over. In a couple of years you may or may not want to replace the scope with something a little better depending on how you like the scope on it. I know lots of guys that never replace them and never have issues, but others like me like nicer scopes. If you ever do change the scope, I'd change the rings too.

The next choice I'd look at is the Marlin XL-7 for the long actions and XS-7 for the short actions. These have a trigger similar to the accu trigger, and seem to be getting really good reviews. You can often find these for around $300, but they don't come with a scope so you would have to add a scope. You could go with a Burris FFII or Vortex Viper and still be in your budget.

There are also other good choices like the Stevens 200 which is basically the old Savage Model 10. The only reason I'd hesitate to recommend these is they are often around $300 with no scope. IMO it's well worth the extra $100 to go to Walmart and get the Savage Model 10 and get the accu trigger and a scope. Heck imo the accu trigger is worth the price difference alone.

These are all inexpensive but not cheap rifles. By that I mean they are inexpensive in price, but not cheap in quality.

The guns to stay away from in this price range are the Remington 710/770 models. These are just pure crap.
The other one that's not as bad, but I'd still stay away from is the Mossberg ATR. There have been reports of a bolt flaw that's ended in some people getting seriously hurt. I'm not sure if they fixed this or not, but I'd not be willing to take a chance. That topped with the fact that you can get a much better gun for a similar price leads me away from this gun.