Of the choices I would recommend .308 or 30-06 for no other reason than the ammunition is available everywhere in a vast array of bullet weights and designs and it is relatively inexpensive.
As to the rifle, you should reconsider buying a new Remington 700. Remington's QC as dropped since the Freedom Group bought them. Alternative brands in the same price range to consider are Savage, TC, Weatherby and Tikka. If you have your heart set on a Remington, find a good used one from before FG started mucking up the works.