I’ll second those advising you to get a Savage. I haven’t priced rifles in a few years, but unless you are going stainless with better quality stocks, there are a number of good rifles out there that come under a thousand dollars. You should be able to find a 700, or a Ruger M77, any number of Savage or Howa rifles. I bet you could find one of the stainless 700s for well under a thousand dollars. Why go with what amounts to a throwaway rifle? Get something you can build on.
A new Ruger in 30-06 is about $650 near me via http://www.galleryofguns.com
A Savage runs about $720. A Browning A-bolt in .308 would run around $800.
A Remington 770 runs about $300, including a scope.
I’d prefer a Browning myself, but I’m sure a 770 would get the job done.