You won't get a turkey for Thanksgiving, because turkey season is in the spring.
But you certainly can get a deer and a hog, or two.
I have killed more than 70 deer, and a dozen hogs, in central Georgia.
I was hunting in Baldwin and Hancock counties. I did a lot of hunting in the Oconee River swamps, lots of hogs down there.
As a rookie, the best thing you can do for yourself is to get a scoped rifle. There are lots of rifles that are good for deer and hogs, a Marlin .30-30, or .35 Remington, a Savage or Remington bolt action 30-06, .270, or .308, and many others.
You will be hunting in brush mostly, unless you get on a power line or a field.
Most of the shots I made were less than 50 yards. I hunted with iron sights and with a scope and the scope was a big advantage.
Get a good scope and practice! Go to the range and practice at 100 yards.
When you are good at targets, get a life size silhouette of a deer and practice on that.
As a rookie, if your hunting buddies hear you take a couple shots, and you don't have a dead deer to show for yourself, you are going to become a very lonely hunter. Far better for you to take no shot at all than to take a bad one and miss, or, worst of all, to wound a deer and it gets away.
The single best thing you can do for yourself is to be a good shot. You should be able, from a rest, to hit a grapefruit five times in a row at 100 yards.
There are lots of wildlife management areas in the state, called WMAs.
Besides your deer license, you just have to buy a WMA stamp for ten or fifteen bucks and you can hunt in any WMA in the state.
Anybody can hunt there and anybody does. They are crowded and some real dumb ass trigger happy guys are found there. I don't like 'em.
Your best bet is to join a club.
If you could find a good club along the Oconee River, or the Ocmulgee River in central Georgia, you will find great deer and hog hunting, and lots of turkeys, too. You could find a club in these areas that is a 2 hour drive from north Fulton County.
Best to stay in state as I can assure you out of state tags are expensive, South Carolina is $245 for an out of state deer license.
Good luck, hunting is a lot of fun and the meat is good. I just love wild hog, it is the best meat on God's green earth.
As to how to find a club, google up "deer hunting club Ocmulgee River" or "Oconee River."
Here is one I found, good deer, hog and turkey hunting near Perry Georgia, $1250 a year.
They have camping so ideally you could go down on Friday at noon and beat rush hour, and hunt all day Saturday and Sunday.
http://www.oakywoodshuntingclub.com/index.html
Here is a club that looks really good in Butts County on the Ocmulgee River, looks like great deer hunting and turkey too. They don't say anything about hogs, you should ask 'em.
$1400 a year and they need 3 members!
http://www.qdmaforums.com/showthread.php?p=144672
Another resource is a magazine called Georgia Outdoor News. This is sold at convenience stores and all gun stores. I am pretty sure you could find a club to join in this magazine, plus lots of other good info. Here is their web site:
http://www.gon.com/page.php?id=54&cid=87
The best hunting is in the central and southern parts of the state, both for deer and hogs.