Mosins....
Here's my take. I have only a minor case of Mosinitis. I only own one, although more are in my future. I like 'em.
91/30: Long gun. Really long. When they've got good bores, they may be the best shooters of the bunch (Finns aside, and you won't find one of those for what you want to spend), but they were also made the longest, and used the most, so the spread of possible bore conditions is huge. You'll get the most velocity out of your ammo, due to the long barrel. Carrying the rifle afield might not be the most fun, due to length, although they're not much heavier than the carbines, and some even may be lighter. Depends on the wood. Did I mention that the 91/30 is a long rifle?
M1938 carbine: Perhaps the best of the three as a field gun, except that the bores can be very rough on these. It's that whole "Great Patriotic War" thing, dontcha know. Many (most?) have been counterbored, drilled out to way over bore diameter from the muzzle back about an inch or so. This can restore accuracy if the muzzle crown is damaged, so it's not necessarily a problem, but... Some M38s had new rifling cut when they were counterbored, taking the diameter from ~.311" to somewhere in the .314-.315" range. Bullets in this diameter will be hard to come by, if you can find them at all. If your barrel is oversized, normal .311" bullets won't shoot worth a darn. Replacement barrels are available, for around $35, plus gunsmith time to install it. If you can get a good M1938, this would probably be the best choice.
M1944 Carbine: All of the good things about the M1938, plus better bore condition (on average), especially on 1950's production Warsaw Pact rifles, since those never saw combat, and were only issued for a few years. The only downside to the M44 as a field gun is the permanently-mounted bayonet. It comes off with a screwdriver, but the mount is integral with the front sight base, and sticks out about an inch from the right side of the barrel. Many M44s shoot to different points of aim with the bayonet extended or retracted, and they were sighted in with the bayonet extended. So, if you remove the bayonet, you may have to adjust the front sight. Some M44s care, some don't. Only your rifle knows for sure. Somebody should make a bipod mount that uses the M44 bayonet mount as an attachment point and takes a standard bipod, but nobody does that I know of.
Don't let anyone talk down the Mosin as a big-game rifle. The 7.62x54R cartridge is closer to the .30-06 than to the .308 in power, and the rifles can certainly be accurate enough for reliable hunting shots. Don't rely on surplus ammo to tell you about the accuracy of your gun. My M44 is a 3" gun at 100 yards with Czech surplus ammo. Using the Winchester softpoint load, the gun shoots much better, at least from field positions at big metal disks. I haven't taken the Winchesters to the range and grouped them yet, but the difference was noticeable in informal 100-200 yard shooting, so I have no doubt that they'll group better.
The rifle's action represents a road not taken by anyone else, and it's not the smoothest by any means. The trigger isn't great, and the safety is just plain weird. But the action is extremely simple, rugged as a shovel, and it works. Ugly guns, but I think they're neat.
My K31 is a far better rifle, but the M44's a keeper. It's going to deer camp as a back-up rifle, and if he hasn't bought anything else by then, my brother will be using it. If he doesn't get his deer, it won't be the gun's fault.
--Shannon