You will not be sorry if you find a K31. They shoot the GP11 milsurp and that is some good stuff. It is pricey. I would imagine it would be cheaper to reload. The GP11 is not reloadable, but it is not corrosive.
Accuracy is top notch. If it had a peep sight system, IMO, like the Enfield, it would be even more accurate. But this rifle will definitely hold its own as far as accuracy goes. I believe Enfields are very accurate rifles as well. But, a lot depends on bore condition and variables like that.
The bolt isn't too hard to disassemble. It will take a few tries before you get good at it. However, bolt removal for cleaning is a piece of cake. Just push the little lever and out it comes.
The action should be fine in the stock it comes in. I wouldn't worry about bedding it. Might help tighten group sizes, but they are already such good shooters as they are, you probably won't need to.
"Unissued/unfired" K31s will probably demand a premium. Many of the K31s I have looked at still had beautiful bores. If you can, inspect for the best bore. They don't have to look good on the outside, to be tack drivers on the inside.
This rifle does take a 6 rd. charging clip. It is made of a flimsy plastic-like cardboard with a very light metal rim. They are easy to use, but pricey if you're going to buy some. IMO, they aren't necessary unless you might be hunting and splurge for a few and some kind of ammo holder just to facilitate faster reloading assuming you don't scope it on the receiver.
I can't attest to ballistics. I don't reload for the rifle, and don't know a lot about the ballistics of the 7.62 NATO round. But, it is a high powered rifle round, and with proper frangible bullets, will have no trouble at all dropping any big game in N. America, so long as you do your part. I would have to guess that ballistics is around the 7.62x54R and .303 British. Here is a link to some ballistics on the 7.5 Swiss:
The Swiss Ammunition Page
I can't think of anything else funky that would need to be dealt with. They have extremely nice 2 stage triggers for a military rifle. The other thing you might find, under the butt plate, is the original troop tag to whom the rifle was issued to. Typically found is a name, and address. Often times is a unit.
These babies are accurate right "out of the box" so to speak. Or right off the rack, unless someone has done something to it. I have not heard of an inaccurate K31, lets put it that way. But, of course to get maximum accuracy, you will need to do some practicing. The straight pull design facilitates a very quick action of reloading a round. The 6 rd box mag is detachable, which I really like the idea of especially when hunting. Here in WA, it is illegal to transport a rifle loaded in a vehicle. Detachable mag is quite nice. I have considered scoping my Enfield for this reason. The only other thing to be aware of is the stocks on these sometimes are beat up. The "beaver chewing" on the butt of the stock is most likely attributed to how the rifles were carried, and used for example, to knock snow off soldiers' boots. This is not an uncommon feature.
Depending on your price range, really nice K31s ought to be under $500 anyways. Probably $400 for some of the nicer ones. Walnut stock K31s seem to demand a higher prices. But, you ought to be able to find a pretty nice one for $200 or $250. I lucked out and found one at a gun show for $125, you bet I snatched that baby up in an instant! But, the price for a Mosin is extremely hard to beat. Accuracy is generally pretty good, but bore condition weighs in. Handloads with proper sized bullets after slugging the barrel, of course, will yield the most accurate results. But, that is true for any rifle.
The only thing is if where you hunt, you need soft point, or frangible bullets, then you might need to hand load. I have never pulled a bullet from any GP11 to replace with soft points. Might be worth buying a couple boxes of Prvi Partisan or some other reloadable 7.5 Swiss with soft points to hunt with, and reload as necessary.