Accuracy will mostly be determined by the rifling in the barrel and the crown. Secondly the fit of the rifle to the stock will be a factor. Too poor of a fit and you'll be all over the place, too tight on the action screws will also affect accuracy. Third, reloading your own ammo is the ultimate key in getting accuracy out of a milsurp. Slugging the bore and trying diferent loads is the ultimate way to tighten up a group.
Mausers have the best actions of any cheaper milsurp. They're smooth and reliable. Mosins are good too but can suffer from what they call sticky bolt syndrome. This is where the bolt gets tight when you try to open it after firing a round. People often blame it on burrs in the chamber from poor machining due to getting the rifles out too quickly to arm the Russians. Others say the bi-metal casings are the problem. Either way its a pain in the ass when you're trying to enjoy shooting.
Both rifles are good for accuracy with the Finnish capture Mosins being better as these are rifles that were either built, or re-arsenalled by the Finnish army. Often you'll find shims under the barrel or action when taking one apart. Its best to pay attention and replace it because it was put there for a reason. I know people who thought it was just garbage paper stuck under the barrel, tossed it, and had poor accuracy from that rifle.
Like mentioned in Soxfan's post, theres really not a lot you can do with these as far as a project rifle. Unless you plan on drilling and tapping for a scope mount or doing custom trigger work, a new stock is pretty much your only option. There are companies that sell scout style scope mounts that replace the rear sight. This allows you to scope the rifle with a long eye relief scope without having to drill the receiver.
Enfields and Swiss K31s are also accurate rifles, usually more so than Mausers and Mosins, especially the K31. Ammo for K31s is a little hard to find but if you stock up for it at gun shows you're all set. SKS' can be tuned for better accuracy but take a little experience in working with semi autos to understand the inner workings to make sure you're shooting a safe rifle. The bolt for example needs to be stripped and cleaned so the firing pin rattles to avoid a potential slam fire problem. Theres a guy from another milsurp forum that does custom trigger work if you mail him your SKS trigger assembly and guarantees better accuracy. Other things like aftermarket stocks and sights will help you with an SKS too.
Just about any comon bolt action milsurp rifle with the exception of the M95 Steyr is easy to take down and work on. Some have better qualities than others but unless you're willing to spend top dollar on a US 03 Springfield, there isn't one that stands out for having best features. Its all in what you feel comfortable shooting. You can buy 2 Mosins and have one be a tack driver while the other groups like a shotgun. My advice is do some reading on sites like surplusrifle.com. Theres info there on take down, cleaning, refinishing, accurizing, scoping, ammo, etc. Then go to a gun show and buy one that speaks to you when you hold it. Just be sure to check for a clean bore and sharp crown. And most importantly read up on cleaning after shooting corrosive ammo to avoid damaging your new milsurp.
Forgot to mention... Finnish capture Mosin Nagants are often easily identified by having an SA in a small square stamped on the receiver. Sometimes you can get lucky and find one at a shop or show that the owner doesn't know is a Finn rifle, hence a cheaper price.
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