Alright Couch Commando.... Here's the "skinny"...
Ive used a WASR 10 with all sorts of ammo to kill deer, hogs, and all sorts of varmints and such.
Before I explain, very very first, the AR and Garand. Both will kill deer. Much to the argument of thousand here, I would say the AR is a little too light for deer unless you are all about shot placement and buying decent expensive ammo. You will wing a lot of deer with an AR unless you are a decent good shot and are willing to spend money on quality ammo. Garand is a killer. 30-06 will mess up a lot of shoulder meat if you're not into real good shot placement. But it will kill the crap out of a deer with soft point ammo DRT nearly everytime. Lots of energy.. I try for headshot when I hunt deer with a Garand and it blows their head open.
Start with the AK rifle: Yes. Your WASR is more than sufficient for the hunting you describe. I seldom see a deer over 100 yards due to the type of woods we have in Texas in my hunting area and yours sounds similar. 4 moa is good enough to get that shoulder broadside shot and make it count. If you like precision shooting, like picking which ear or eye you're going to hit, that's another story, but that's not what you're asking. Consider the side mount for a scope mount. Midwest makes an awesome one. Throw a decent scope on it and you have yourself a good deer gun for small dollars. Redneck up!
Now the ammo. I have shot a LOT of Wolf of all types. Soft point is most effective, but understand, it's cheap soft point and some of the time the bullet will look like a long string of melted candle wax, like a worm, when you're cleaning out the deer and find it. There is a name for this but I do not know it. It is a failure of the bullet to mushroom. It just simply gets skinny and reduces in outer diameter rather than retaining the outer diameter and mushrooming at the top. It is not ideal, but you still have a relatively good hit. You'll sometimes find the soft point part of the bullet, and the hard casing of the bullet, both in the animal but in different places. It makes less shock and a smaller wound cavity than better soft point ammo. But hey! I dug this out of a dead animal so it doesn't suck too bad!
Wolf hollow point is in 2nd place. Frequently it will just break apart into fragments. Most of the time you get good expansion and it stays in tact. But somewhere in the less than 50% range but greater than 10% range, you'll just have slivers of metal left and no bullet.
FMJ is FMJ. Pokes holes and doesn't do well relative to your other options. Ive shot pigs 2,3,4 times with FMJ from a moving vehicle across a plowed field and watched them keep running. Close enough to hit them with a rock. I could see the entry wounds. Bullets were just zipping thru them. They WILL die, just not "DRT" or anywhere you could find them. I shot a pig with a 30-06 FMJ out of a Garand in the hip while it was running and it was still able to see me, change direction, charge me and make it all the way to me before getting killed at close range. 30-06 soft point however would have blown his ass end apart and he would have been going no where.
Good hunting!