My experience with Russian Mosins is that they do about 4" groups at 100 yards. That is enough for deer hunting within 100 yards.
The Finnish Mosins are a different story. Many of them are sub 2" at 100. But those cost more coin.
Usually with a little care, the Yugos will do 2" at 100. The problem with them is that the sights are set up for long shots, and many of them will be quite high with the factory sights. That's easily fixable, but it's one more step.
BTW, I reload for all of the above.
The full-length Mosins are pretty heavy. The M44 is lighter, but I'd still think seriously about cutting and grinding off the bayonet lug to lose a few ounces of steel if I still had one.
If the objective is the least expensive thing that will put venison in the locker, then the Mosin is the ticket.
If you just enjoy shooting milsurp, and want a gun that is a lot prettier than a Mosin and more amenable to upgrades, then a Yugo 24/47 or an M48 is the ticket.
If you want something that is lighter and more accurate, then I'd look around for a good used Savage or one of the newer entry level rifles. Here is one possible alternative:
http://www.ksl.com/index.php?nid=218&ad=21012609&cat=377&lpid=1&search=savage
Another choice that has not been mentioned is the bolt action 30-30s made under the Savage and Stevens names. They can be had for under $200, they are 2" or so shooters, and completely satisfactory for deer inside 125 yards or so. They are also low recoil, and a lot of fun to shoot. I shoot cast lead in mine, which makes them also very cheap to operate.