BC means more than the average guy thinks when you're shooting at 700+. Our buddy shoots a 220 swift out to 500 yards. His bullets get there in a hurry although they can get blown around a lot. Past that my 6.5x284 with a bullet that's almost 3 times as heavy shoots flatter, drifts less, and of course hits a lot harder! You really need to do some research into the types of bullets you want to shoot. BC's will vary considerably even in the same bullet weight for caliber. IE, from .545 for the 140AMax vs .595 for the bullet I'm shooting. There are 6.5 bullets with bc's over 6. Of course you need to experiment with what bullet your gun likes best but be forewarned that just because your gun will shoot a bullet into one hole at 100 yds doesn't mean that it will shoot even moa at 700. You really need to shoot alot at different ranges to determine what your equipment but more importantly you are capable of. I still believe that my gun can shoot better than I can shoot it. That being said I've shot 3/4" groups at 300 yds and 2 1/2" groups at 700. Here's one way to think of it: what's the difference if you shoot a 140 grain bullet through a deer at 50yds or at 800yds? If the bullet passes through, expands, and dumps it's energy in the deer; distance doesn't matter. You do have to shoot a bullet that will still expand at the expected impact velocity. That's why you'll see most long range hunters shooting match bullets. The Amax and Bergers work EXTREMELY well. We've seen exit holes of 2" at 700yds with both bullets.
Experiment, develop your drop chart, and start shooting targets until you know that you can hit them. Everyone here has probably read about us shooting deer to 800yds or so. As Petey said, we've knocked them over with my 6.5 that far. BUT, none of us has ever taken a shot that we didn't know we could make. How did we know? We shoot at jugs, steel, and groundhogs all summer from 300 to 1200 yds. We have to drive around an hour to do any of that but when we find a deer feeding at 750, the confidence that you have looking through your scope goes a long way into making that perfect shot.
In reference to the Savage and 308, both work great and would be a great platform to start into this endeavor. Spend more money on optics and later on if you get hooked like I have, build a custom gun just for you. Until then, let me know if I can help.