A typical mosin will print groups about the same as an SKS (some out there do FAAARRR better - MOA or less - country of origin matters), but it's got a far greater powder load behind the same caliber bullet. If you want a hunting rifle, the SKS isn't full powered, while the Mosin Nagant is.
You could look into other milsurp rifles from Big 5, too, if you've got one of those locally. A Schmidt-Rubin K31 straight pull bolt action rifle is supposedly one of the most accurate of the lot, although ammo is at least a full $1 per round. I've actually heard the K31 is the favorite for the milsurp competition in Sacramento because of its accuracy (i'm near there). That competition goes from 50 yards out to... 500? 600? It's out there a ways, anyway.
The Mosin would be good for hunting dear out to about 400 yards if your gun is accurate enough and you're a good enough shot. I wouldn't reccomend beyond 250, but at 150, the mosin could really shine, yeah. An M44 could fit your bill - short, light enough, but accurate as heck.