If you have your heart set on a Remington, buy a used 700 from before The Freedom Group bought them and quality control went to hell. If you will consider other brands, you may want to look at the Weatherby Vanguard S2, Tikka T3, Savage 11/111 or TC Icon. They are new and do not have much of a track record, but there is also a lot of good press on the Ruger American.
As to caliber, I would go with .308 or 30-06. You can find both calibers with a myriad of bullet weights and types, just about anywhere for a reasonable price.