I'd have to agree with the other posters, it sounds like you need something in the .308/270/30-06 range. The Ruger American Rifle seems to be a screaming deal right now, low $300's with great reviews and excellent accuracy. They are also really light, which can be a pro and a con, although the reports I've read seem to suggest that Ruger's recoil pad works pretty well.
Tikka's are also an excellent rifle, but a new one will probably run you $200 over the Ruger. Howa's can be had for just a little above the Ruger from places like CDNN, and are by all accounts a solid rifle. Vanguards, and Vanguard S2's (also made by Howa) would also be good options. I'm not a huge fan of Savages, but there is no denying that Savage makes an accurate, high quality rifle for a great price.
I don't think you could go wrong with any of the brands mentioned above, but the Ruger just seems like a great value currently.