Like almost all C&R military surplus firearms, it's kind of a crap shoot. I have several Mosins, 91/30 91/59/ M44. All have acceptable to excellent accuracy. One of my sons 91/30 Mosins is what is known as an X-sniper. The mounting holes for the scope mount have been filled, and the rifle then re-finished and a bolt with a straight handle installed. This was done for one of two reasons. 1. The sniper rifles were not need as much as standard infantry models so they were converted to be re-issued to soldiers. 2. The accuracy was unacceptable for sniper purposes, and the rifle was converted, refinished, and put in storage in case the need for more rifles arose.
As far as a deer rifle You might want to look into the shorter M38 version.
The Finn Mosins are much more desirable as collectors, and in a lot of instances are better shooters, but also are priced 3 or 4 times higher than the Russian and other Soviet Block rifles.
For more information try:
http://milsurpshooter.net/
Sporter stocks are available. Also scope mounting kits that include a new bolt handle that has to be screwed on the bolt after the original straight handle is cut off, and a mounting hole drilled and tapped. The easiest way to install a scope is with a "scout mount" that attaches to the rear sight hardware, and requires a long eye relief scope.
7.62X54R ammo is available in a soft point round for hunting. There is still a lot of relatively inexpensive military surplus ammo available for practice. Consider ALL military surplus ammunition as corrosive, and proper cleaning is
manditory as soon as possible after shooting.
Really fun and interesting guns to own and shoot. Inexpensive to buy and shoot.