So does your $600 budget include optics or not? If $600 total is the max you can spend? Do you want a bolt action or a lever action?
If you want a bolt action,
I'd look into one of the Savage Model 10/110 in .243, 270, 30-06, or your choice of caliber that they sell with the accu trigger at Walmart for right under $400 with a cheap scope. I'd then either sell that scope, or keep it for a secondary gun. Then I'd use the rest of the money to buy a quality set of rings and a scope. There are a few good scope choices in the $200 range. My favorite is the Burris FFII's, but you can also sometimes get Nikon Monarch UCC's on sale for $200 that are also good choices, as well as the Vortex Diamondbacks, and the 2-7 Viper that's on clearance. Any of those would be a good choice for a scope in that price range, and then I'd look for a set of Burris Signature Zee rings. They are my favorite rings I've used for the price. I've also used Leupold rings, and while I like them, I think the Burris rings are better as the eliminate the need for lapping, if you need to shim the scope, you can with inserts, and they don't leave ring marks. All of this for a similar price to the Leupolds. They go for around $30-35 in this area. To me these are about the best you can get for under $100, and for a rifle like this I don't think there is a need to buy an expensive pair of rings like Seekins or Badgers.
Another option I'd have previously recommended was the Marlin XL/XS-7, but since Remington made Marlin switch plants, there have been a lot of reports of problems. Enough that I think the Savage is a much better rifle for a similar price.
There is also the Stevens 200 that is basically an older Savage 110 without the accu trigger. These go for $300 without a scope in this area, although Academy sometimes has put select calibers on sale for as low as $179. This is also a good choice, but imo at $300 it's worth paying the extra $100 for the accu trigger and the $30 scope. That's just my opinion though.
If you want a lever action, there are also lots of good choices from Marlin, Winchester, etc. If it was a Marlin though, I'd try to find an older one. The newer ones are having major quality issues, and they actually suspended production of their lever actions right now for the rest of the year so that they could work on their issues.
If your $600 budget is for just the rifle, you open up many more good options. Some I'd check out in this price range are the Tikka T3, any of the Savage models depending on which style you like, some of Weatherbys offerings, or the Browning X Bolt hunters. All of these are good choices and you really can't go wrong with any of them, so see which one fits you best.
If you insist on a Remington, I'd get an older one, but with all of the quality issues they have had the last few years, I'd not recommend one at all. If you do get one and happen to get a good one it's great, but if you get a bad one which there seems to be a high chance of, you get to deal with this sort of customer service.
http://www.snipershide.com/forum/ubb...02#Post2823702
That combined with the fact that you can get several other better rifles from companies with great customer service for a similar price makes the current Remington offerings a bad choice imo. Remington is now owned by an investment group that seems to just care about the rate they can turn out guns, and not about the quality. Sadly Remington also acquired Marlin in 2007, and shortly after their quality too a steep dive downhill too. They also own several other companies.
Old Remington products are great though, if you want a used rifle and really want a Remington. There are just so many others that have come such a long way over the years, while Remington has been taking huge steps backwards.
Overall, though it just depends on what you want, what fits you best, and what you can afford. You are much better off buying a $300 Stevens or similar with a decent scope than you would be with a $600 rifle with a $30 scope on it.