There are lots of good choices for the application you mention. The one you're thinking about is undoubtedly a good choice.
Savage has the reputation of having the best out of box accuracy, among the people I generally hear from.
30-06 is a splendid round. 308 is just the same cartridge, with a shorter case, operated at higher pressure, for very close to the same muzzle velocity. Either will do fine. The 30-06 gives you just a bit more "reach".
Just my own bias: The 30-06 and the 308 are both fun to shoot for the first few shots. But most people quit having fun after the first 15-20 shots. So you won't take either to the range a lot, to just shoot for fun. Also, both cartridges are more powerful than you need for 95% of the available hunting in North America. If you plan to use the rifle for fun trips to the range, you might think about the Savage Axis in 7mm-08. It has plenty of range and punch, and you'll enjoy trips to the range a lot more.
I've seen a couple of scoped Axis rifles on the local ads for $275-325.