If we're talking Eastern NC, a .30-30 will work well, unless you hunt from a stand on the edge of a crop field. Stalking, or woods stands will NOT have long shots, but a fast follow-up is often handy. I assume we're talking whitetail here. And even our biggest "predators", Black Bears, are small enough a .30-30 will handle them. Buffalo Bore makes some heavy .30-30 loads if lethality is a concern.
I live along the I95 corridor, and there aren't a hell of a lot of places to hunt where the trees are over 200 yards apart, excepting the aforementioned agricultural fields. I don't have the time to hunt these days, but the .30-30 bagged me a few in my younger days, and more than a few for my father. And while an uncle got in trouble for shooting a whitetail on a cops lawn with the .30-30 he kept behind the bench of his truck, that's hardly the rifle's fault.
The 7mm is a great round. I'm not sure I'd take the extra muzzle blast, expense, and trouble reloading a belted magnum over something like a .270, but if I were out West, it would be one of my top choices. Here in NC though, it's advantages are wasted. Anything over a .270 or .30-06 is really just putting lipstick on a pig.
Check the used gun racks at local gun stores. You can find old Win 94s and Marlin 336s for a couple hundred bucks. I've seen older Savage 110s in the $300 range as well. It just takes patience and disposable income.
ETA: One advantage i don't think I saw mentioned was how handy the .30-30s are. They are kinda heavy, but they tend to be compact enough to handle well in the woods out here.