Right now....I'd say it'd be best to go with the .30-06. Greek surplus ammo for it is fairly cheap atm. 7.62x51* surplus on the other hand has gone up in price, for various reasons.
However, once the Greek .30-06 dries up, then that's it. As far as I know, there aren't any countries still fielding .30-06's. 7.62x51 is still a NATO standard, however, so there will be milsurp for that for some time to come.
As for the rifle: for under $500, you're looking at Savages, Stevens, and Remington 700 SPS's, The Stevens are probably the best value; they're nearly identical to the Savages, just without the Accutrigger, and IIRC they're under $300 or so.
The AccuTrigger on the Savage 11/111's are pretty nice, and allow you to adjust for the trigger pull weight. These are more expensive than the Stevens, but less than the Remington.
The Remington 700 SPS has the advantage of having the most aftermarket accessories available. These are a bit more expensive than the Savage, and lack an easily adjustable trigger. I bought one in February for about $480.00, chambered in .30-06.
All three are probably just about as accurate out of the box. Many Savage owners claim that they're more accurate, but I haven't really seen any comprehensive testing to verify that claim.
My suggestion is to go to a store and handle all three. It was the handling characteristics that made me go for the Remington over the Savage. However, what I think a gun should handle like is a personal preference, and I tend to go towards heavier and more tightly built rifles as opposed to lighter, somewhat "looser" built ones.
*7.62x51 NATO is nearly identical to .308 Winchester, and can be fired in any firearm chambered for .308 Win.