Georgiahunter, .308 or .270 should suit the need nicely in Georgia woods or over clearcuts. As far as the brand of the rifle, it's sort of what fits your budget. Personally, I'm a Remington fan with the bolt gun and M1A with the autoloader.
I have owned and shot whitetails with both calibers. I hunt in Missouri, and shots are under 150 yards. I prefer the .308 Win, and it's siblings (7mm-08, .243) hands down. Less recoil and short action. I use a Marlin XS7 in .308 and love it.
If you are hunting over bean fields and taking 200yd+ shots than the .30-06 family (.270, .25-06) has an advantage.
As far as optics... Nikon Prostaff or Redfield Revolution in 3-9x40 is hard to beat for the money.
Winchester 100 .243; Marlin XS7 .308; Stevens 200 .223; Rossi 92 .45LC; Marlin 1894C .357M; Marlin 30AS .30-30; NEF Pardner Pump 12ga; Mossberg 500 Turkey 20ga; Winchester 1200 20ga; Savage Mark II F .22LR; Henry H001 .22LR; Marlin 60SB .22LR; Ruger 10/22 DSP .22LR; Browning SA-22 .22LR; Savage 93R17 GV .17HMR; Remington Genesis .50 cal ML; Ruger SR1911 .45ACP; Ruger Vaquero .45LC; Ruger Blackhawk .357M; Ruger SR9c 9mm; Ruger Single-Six .22LR; Browning Buck Mark Camper .22LR
I just received a new remington 750,308 cal,and theirs rust spots on the barrel,also the recoil pad looks like a kid installed it,doesn't line up with the but of the gun!I keep trying to call remington,but can't seem get anyone to talk to about it.