I don't own a Mod 44, but do have a couple mod 38's and a 91/30. I find that they each shoot very well with cheapo gun show ammo. I don't use surplus corrosive ammo. Usually I can find Olympic brand made in Greece for a decent price. Olympic offers soft point ammo and brass cases. I've shot the Winchester white box brand with good results, but its a bit expensive.
Many feel recoil is an issue with the carbines. I've not found it to be a problem. I place it somewhere between a .308 and .30-06, about where it should be.
At the prices Mosins can be obtained for, it's hard to go wrong with purchasing one for any reason. The fact that they are a ready made deer rifle is a plus. Be sure to completely disassemble it and give it a thorough cleaning, even if it looks clean already! Every example I've purchased has presented a cleaned appearance. However, each one still had cosmoline deep inside the recesses, including, and most importantly, the bolt.
Check some of the surplus military rifle sites for details on proper dis-assembly, cleaning and care.
This is a good place to begin:
www.surplusrifle.com