1) NC does have reciprocity with GA. Since NC requires a class, it actually has reciprocity with more states than GA does, because GA does not require a class. (Many, but not all, states only extend reciprocity to other states with similar requirements to their own; this is why NC has reciprocity with WV and SC, and GA does not; the fact that I have had plenty of classes between the military and the state of FL does not help me use my GA permit in either of those states.)
1a) A friend of mine near Asheville has had some difficulty finding a class he could take, between class availability and his own work schedule. Hopefully, you can time things so your visit home will work. Good luck, get on it ahead of time, as you are doing.
2) GA does not require handgun registration. You don't have to do anything to bring your handgun from NC. However, NC does require a pistol purchase permit, so when you go home you will need to go to the sheriff's department with your proof of residence, pay your $5, and get your purchase permit. Note: This is one permit per weapon.
3) I'm not sure what the waiting period requirement is in NC if you don't have your carry permit - IE I don't know if the purchase permit from the sheriff's department waives a waiting period, but I suspect it does not. So, you may not be able to buy your pistol prior to your CCW class. When I took my class in FL, the range there offered loaner pistols for the practical portion. If the range where you take your class does not, you might be able to borrow one from a friend. Note: Federal prohibitions against interstate transfer of possession of handguns do not apply to loans, only to actual transfers of ownership, so you could borrow one from a friend in GA.
4) The list people have given you so far for recommended used revolvers has included the S&W 19 (the 66 is the stainless version), Ruger GP100, and Ruger Security Six in .357 magnum, and the S&W 15 in .38 Special. These are all good choices. The S&W models listed all have adjustable sights, and are K-Frames (relatively light). There are similar fixed-sight models on the market, too, but the model numbers are slightly different. Another good revolver would be the S&W 686, but finding one in your price range would be tougher.
Since you are looking at using the revolver for SD, HD, and camping / outdoors use in black bear country, I personally would not go any smaller than a 4" barrel. You get a significant drop in velocity, and increase in recoil, as you go shorter than that. If your primary use were to be as a woods gun, I'd recommend a 6" barrel, because at that length the magnum rounds really start to shine.
(Then again, I don't like the balance of 6" barrels, so I still use a 4", but my woods gun is a .44)
Cheers,
M