RE: Mosin Nagant 91/30
There are threerelative weaknesses that stand out in my mind: the stock does not fit large framed shooters well, the sights can be difficult to zero properly without modification (and scope mount kits are expensive), and decent hunting ammo can be hard to come by if you don't special order and stock up.
As far as capability to take medium game, it'll get the job done fine. Ballistically the 7.62x54R is pretty close to the .308, which is plenty for deer and the like.
Another milsurp you might want to consider is the Swiss K31. Shoots the 7.5x55 Swisscartridge, which is in the same ballpark of the .308. Hunting ammo isn't much easier to find, but the rifle is made with excellent quality and shoot very nicely.