I'm going to throw in here and recommend a K31, too. Get 'em while you can.
Good history behind the model. If its been used in an important historical event, cool. I like things with good stories behind them. Something that can be hung up on the wall in addition to being used occasionally.
There's
nothing cooler than pulling off the metal buttplate and finding the tag with the name of the original trooper it was issued to.
"I know which soldier this rifle was issued to" is ... well, it's a feeling quite unlike anything else you'll get when buying a military surplus rifle.
As far as inherent accuracy there are few bolt action surplus rifles that come even
remotely close to a well maintained K31 and surplus GP11 ammo.
As far as the other guns, I own a few but haven't shot them nearly as much.
I've got a Spanish Mauser in 7x57 - it's a fun gun to shoot, but
REALLY long. Not really something I'd want to lug around all day on a hunt. 7x57 is easy to load for, and supplies are still everywhere - not really in too high of demand. (A year ago I bought a dusty pile of boxes at a local pawn shop - 1,000 Sierra match projectiles the pawn shop owner had got at an estate sale, for a ridiculously stupid low price.)
The opposite end of that spectrum is the Mosin M44. It's a comparatively diminutive gun to the 7x57 Mauser, but it's kind of brutal to shoot. Feel free to be manly and say "that don't bother me!" like I did with heavy hitting rifles for the last 20 years, but you might end up with a ruined strong side shoulder that needs surgery for your trouble, like me...
(Yes, I'm recommending a recoil pad on all of these...)
The Enfield is a neat gun but it's getting a little pricier to load for, and
safe surplus ammo is pretty much gone for good. Also as mentioned above they aren't all as friendly with your brass. (Neck sizing goes a long way, for that, though)
Another one not mentioned yet, if you can find one that hasn't been bubba'd to death, in that price range you are looking for is a 1898 Krag. Great history behind them, and you will NEVER EVER work a smoother bolt action in your life,
period. As far as shooting goes, mine remains unfired - been meaning to rectify that but it's been a safe queen so far. (I do like caressing it from time to time....
)
Keep your eye out for a good '03 springfield, though. I picked mine up 2 1/2 years ago at a local pawn shop for $500 (if I recall properly) and it's in excellent condition. It's a low serial # receiver so I won't shoot it, but the thing is beautiful. I've been looking for one with a higher serial # I can shoot full power loads through. (Yes, I know, mine has probably been through at least two wars and SHOULD be just fine, but ... there's that whole heat treating thing, and I sort of like the way my face is arranged)
Edit to add: One final warning - buying old guns is dangerously addictive! Before you know it you'll have a whole pile of the things to hoard over! You might be better off buying a modern gun without any history or story behind it that you can just throw in a dark corner and forget about in between outings!