RE: AK-47 OR M-44 Nagant(opinions)
The AK is closer ballistically to a 30-30 then a .223. If you can find an AK that is accurate I think it would make an ok deer rifle at short to medium distances. You might have to find or make a 5 round clip for it though depending on where you live. Some states don't allow semi autos at all either, you should check first. I used to have a SKS that I would have hunted with. The AK's actions are unstoppable, so you would never have to worry about it not going off. I had a siaga which is a sporterized version of the AK, but made in the same factory. It was a complete POS as far as accuracy and the trigger was the worst I have ever felt. It was only 200 bucks though.
For that kind of money you could get a H&R handi rifle.
I don't have any experiance with the M-44. I did have a 98 mauser in 8 mm that was an exellent rifle. I owned it in the military and ended up giving it to a good friend for christmas that was always eyeballing it. He was a hunter and I was not at the time, I just liked the way it looked.
I personally would get a good SKS before an AK myself after having both and shooting others. I have actually shot a full auto AK before, pretty cool, but again was not all that accurate.
Good luck,
Paul