The 7mm mag caliber will work fine. But, the rifle might not be the best choice. 7mm mags generally have long barrels, and long barrels are a pain in the butt when trying to sneak through some thick brush. 7mm-08, 308, or 6.5 would be great for the short receiver and shorter barrels. I have iron sights on my rifles and I know a lot of people hunt the southeast with just a scope. I don't know where you will be hunting, but there is some thick stuff in Florida, and iron sights are better than a scope in that situation.
I read a comment advising a medium bore and I am all for it. Bigger and slower moving bullets anchor dear and do it with less damage. 9.3x62, 35 Whelen, 375 H&H, and others would be ideal.
Consider a lever action. They can be ideal for thick stuff.
Finally, if you plan to hunt Georgia some, consider hunting the North Georgia mountains. We got big mountain bucks, hogs, and bears. Please come and get some of these bears. A medium bore is just the ticket for the mountains.