First off Im in Eastern NC I have never hunted. So far I have taken the hunters safety course but thats about it.

What ever you hunt with just make sure you use a good bullet. Don't use full metal jackets. You can use the AR 15 but make sure you use a premium bullet like the Federal Fusions or Barnes TSX. The Mosin is plenty enough round for deer, but I'm not sure what kind of hunting bullets are offered in the caliber. The SKS can be used, but once again use a good bullet like the Hornady 7.62X39 123 gr SST bullet.

For your caliber I really like my Remington Model 7 in 7mm08 Rem. It's basically a .308 Win necked down to 7mm. I reload so finding ammo at stores is not a concern. It's a popular caliber and most stores have it. The 308 Win will kill anything you hunt in NC and ammo can be found everywhere. I also hunt with my AR-15 in 6.8 SPC. Use good hunting bullets and you wan't have any problems with what ever caliber you decide on. Savage makes a good gun at reasonable prices. I'd credit them for forcing other manufacturers to putting better triggers in their rifles. The Savage accutrigger is a good trigger for a factory rifle.

Public land hunting is tough and it will be even tougher if it's your first time. Pick up a few books to read about deer behavior. Then go scout areas to find deer sign. The first week on public land the deer will know it's hunting season and then they basically go nocturnal. So, the best times to hunt are in the early morning or late afternoon. However, I've shot lots of deer between 10:30 AM and 2 PM. So, I'm a believer in the midday hunt. Most hunters leave the woods in the morning and come back in the afternoon.

You want to hunt areas where thick cut over meets hardwoods or full grown pine trees. Also, hunt areas where pine trees and hardwoods meet. Deer like to travel these transition areas. Early season look for white oak acorns (deer love them). After the season starts and the deer are aware it's hunting season they will seek out the thickest places to hide and bed. Try to find these areas and hunt on the edges. Google Earth is your friend for finding places to hunt or at least find areas that look interesting. Always hunt with the wind in your face. If the wind isn't right for a certain area don't hunt it. Shower in a scent free soap and wash hunting clothes in scent free detergent.

Your best bet would be to go to the pay to hunt place, since they do bait the deer. You'll have a higher chance of success. You might could find a local hunting club that's looking for members.

Before you kill a deer call around to some deer processing places and see if they will clean the deer for you. There is a place near me that does deer processing and they charge $20 to clean the deer. I just drag the deer to the truck and take it to them. It's well worth $20 to me for them do it.

I'd invite you to go hunting with me, but I'm in the Western part of the state. The deer numbers in Eastern NC are much better than the Western counties. I'll be trying my hand at public land hunting in the mountains this year.

Any rifle option will work, just get expanding bullets. I've dropped a few with .223 Federal American Eagle, so you don't have to spend $1.50-2.00 a round. <---- Only because I left my Hornadys at home. If you hunt public land, double check the regulations for that particular area, they may be different from state regs. And if you do harvest an animal, at least gut it in the field before taking it to a processor. A hunting ranch will probably have guides to do this work for you.

Mosin, SKS or AR would all work, provided you use the right bullet.  Do a search on "7.62x39" and you'll find multiple threads where guys report great success using steel case soft points.  Hornady also makes a steel case 7.62x39 with their excellent SST bullet.  Site sponsor SGAmmo.com has these for a very reasonable price.  If your state allows .223 for deer (some don't, VA is one), then there's a tacked thread for this one.  Pick a decent soft point or Barnes bullet and your AR would be fine.  Finally, I can't imagine a soft point 7.62x54R not doing the job so the Mosin is an option.  You don't need another rifle, unless of course you want an excuse to buy another rifle...    

As far as places to hunt, check and see if your state has managed, lottery hunts on state lands.  If so it might not be too late to put your name in.  I do this in Virginia, and it's a nice option to get access to hunt land that is otherwise prohibited. You can also find some public land and then try to take off some time during the week to go hunting. There are all sorts of bad stories about hunting public land, and to be honest, there's definitely some truth to them.  But mostly this applies to the weekends, when most everyone goes hunting.  A lot of public hunting lands are relatively quiet on say a Wednesday as opposed to a Saturday.

Look up deer processors in your area.  If you get a deer, field dress it and bring it to the processor.  

Most important, if you want to hunt then you need to get out and hunt.  Even if it's on public land where your odds are long you are still hunting.  You'll learn a lot of basic hunting skills even without any success.  Once you start hunting look for local or regional hunting forums and network with other hunters in your area.

Where in E. NC do you live?

Ok. This has probably been covered, but here goes.
1. Any of those guns are fine with expanding ammo.
2. Practice off hand, field expedient rest. (tree limb, prone,) and limit your shots to your effective range.
3. Find National Forest lands and WMAs in your area.
4. When you first start hunting, find edges, travel routes, bedding areas, feeding areas. Walk a lot, and learn. Read all that you can.
5. After you kill your deer, gut it, and cool the carcass as quickly as possible. A frozen gallon milk jug or two in the body cavity works fine.
6. Find a deer processor and you can have sausage, burger, steaks, roasts and the like.
7. Good luck,