The K-31 is by far the nicest of the four. Doesn't seem like a "surplus" rifle at all. You can find plenty of soft point ammo online that's appropriate for deer hunting.
The Mosin would be the cheapest option. They're built like tanks, but quality will vary significantly. Adjusting the sights (particularly the front) can be a P.I.T.A, but I'd feel comfortable hunting with mine out to about 120 yds.
Friend of mine has an Enfield No 4 that he's hunted with since he was a kid and loves it. He sometimes has trouble finding ammo.
Sorry, but I don't have any first hand experience with the Arisaka, so I can't tell you there.
Bottom line, I'd go with the Schmidt-Rubin K-31 if I had the choice, but either the Enfield or the Mosin would be a lot of fun.
Z