I own all three of those rifles: the K31 (my first rifle purchase, incidentally), an actual German (not Yugo) K98, and an arsenal refinished M44 (and 91/30).
Of the three types, the only ones that have given me any trouble whatsoever are the Mosins. I was fortunate (or meticulous) enough to avoid stuck bolt syndrome in both of my rifles, but I have had feeding problems with both of them. The Mosin magazine is a very simple affair: a flat spring with a narrow piece of steel at the top that pushes the rounds upwards. From time to time, a cartridge will get caught on the lip of the chamber (especially when the magazine is full), which requires a bit of fiddling with the bolt and one's fingers to unjam. From what I can see, the lose tolerances of these rifles occasionally allow the tip of a cartridge to wander forward and catch the bottom of the chamber from underneath. Sometimes, the lip of the brass where it meets the bullet will actually get caught - though this might have more to do with the cheap surplus I'm using than the gun itself. FWIW, both of my Mosins are original factory-matching rifles (i.e. receiver, buttplate, magazine floor plate, and bolt).
I'll second what the others have said about the performance of the M44: it's a lot of fun (especially because it fires the cheapest surplus rifle round available), but it leaves something to be desired in terms of accuracy. If you want a Mosin that will actually shoot well, you'll probably have better luck with a 91/30 or, better yet, a Finn. Thing is, you can get a K31 or a Yugo Mauser for a lot less than a decent Finn, so the Finns tend to be more attractive to Mosin enthusiasts. I use my M44 as a blasting/plinking rifle, because it's pretty useless for serious target shooting beyond 50 meters.
I don't know how the K31 would perform will perform when subjected to the elements, but I've never had a problem with it otherwise. If and when I finally try deer hunting, that will most likely be the rifle that I take.
The Mauser 98 is a solid design all around with few (if any) significant flaws.
FWIW, my next Milsurp purchase will probably be an Enfield, if I can find one for a decent price.