Most accurate Mil-surps:
1) Either a 1903/03A3 or K-31. Despite all of the negative comments I have heard from people regarding the fact that the 03A3 isn't machined from solid-stock (and as such is considered inferior) it is easily more accurate than I. The K-31 is nice and has a trigger as smooth as my target AR. Downside of both are the issue sights. K-31 open sights are tough to manage when accustomed to apeture of 03A3/M-1/et al but the 03A3's sights can't be adjusted to the center of the target.
2) M-1 Garand with proper ammunition. Sights can be adjusted to center impact better than with 03A3, but I find this rifle to be more sensitive to position variations when firing sling-supported.
3) Likely a Mauser variant. Not all Mausers are created equal though, and I have never fired an M-96 Swede. My Mauser experience has been with M98 types in 8mm.
4) M-44, Russian, I think. Loud, fiery, fierce, shoots ok, not great. Distant last on my list of mil-surp bolt guns.