old topic but worth reviving.
The best milsurp to groom into a hunting rifle is a Mauser 98, or Mauser 92-95, period. Add an $80 stock to a WWII K98 and you have as good a hunting rifle as you can buy anywhere, and to get that controlled feed design today, you'd have to spend $1000 for a new FN-made Winchester Model 70. You can buy a sporterized S. American Model 98 for $150-$250 to build from. I bought a 7.65 x 53 Peruvian Mauser that had an aftermarket trigger, side safety, synthetic stock, drilled/tapped/scope mount but no scope, bent down bolt handle, for only $154 out the door, and that included a box of 50 shells ammo. The gun would shoot a 3/4" group at 100 yards, I sold it for $250 easily on GB and the buyer loves it- what more can you ask for ? It was a trade-in at the gun shop.
If you want SMLE, that Jungle Carbine is the way to go. It's practically ready to hunt with as issued, lighter, handier, and short barrel. I have all 3 of the popular SMLE's- No. 1 Mk. III*, No. 4 Mk. I, and No. 5 Mk. I Jungle Carbine. All are 1940's WWII vintage.
The only one I've fired a lot so far, was the No. 4 Mk. I The truth is, all SMLE's suffer from "wandering zero" to some extent, because they are not bedded tightly into the fore end stock, and the stock is a 2-piece design. The buttstock screws into the action receiver with one long bolt, and the action is then clamped into the fore end by the front barrel band and magazine/trigger guard assembly. You can grab an SMLE barrel and move it around quite a bit in the stock- and that's exactly what happens when you shoot it, and the barrel begins to get hot and expand.
All the milsurps suffer from this trait to some extent, and many hunting rifles as well- being production line items, they weren't carefully bedded into the stock with tight tolerances for maximum accuracy.
The SMLE could use a little "accurizing" as issued. I took the No. 4 Mk. I and Acra-glass bedded it into the fore end stock. This is a slightly messy job, as the fiberglas resin runs out of all the small cracks, and must be wiped away after you clamp the barreled action back into the fore end- and the barrel must first be painted with release agent- but it can be done at home on your workbench or kitchen table.
After bedding, the gun became much more accurate and held zero much better. It only wandered slightly, i.e. the group will move up to the left as the barrel gets hot- but acceptable.
This is not unusual for any gun. I have a Browning A-bolt Gold Medallion in 7mm Rem Mag that puts the 3 first shots in one hole at 100 yards, then subsequent shots and groups open up a bit as the barrel gets hot. Perfectly normal- the barrel expands and moves, and has to go somewhere- typically it moves upward. So it even happens with new $600 hunting rifles.
Bed the barrel on an SMLE, then fire form/neck size/reload for that specific rifle, you'll have as accurate a hunting rifle as you'll ever need. For one shot game kills under 100 yards, the SMLE would work as issued- because they won't get hot enough to wander the zero, and you're only firing one shot. If you don't want to accurize it, you'll have to sight it in COLD. Then wait until it cools down again, then continue to sight it in. Because if you keep moving the sights around as it gets hot, it will not shoot there when it cools down again and the barrel contracts. This means fire 3 shots, move the zero, then wait 1/2 hour for it to completely cool down, then fire another group and check it. You want to simulate a cold gun condition that you just walked into the woods with for deer season.
The Mosin Nagant isn't even in the same class as a Mauser or SMLE. I've seen those at gun shows for $125 with 5 boxes of ammo, and a custom stock/scope- with no buyers. They are just crude weapons- but they too can be made accurate. You can accurize anything, it's just a matter of money and time. A Mosin Nagant is about the cheapest milsurp you can buy- to be honest I'd take a Jap Type 99 or Type 38, over a Mosin.
One big advantage of the SMLE, it has a quicker action than a Mauser or Springfield, and has a shorter bolt throw, and a large magazine capacity. R. Lee Emery just did a shootout between Springfield and SMLE on dinner plates, and the Aussie shooting the SMLE beat him easily. They had to break 20 plates in the quickest time from prone position. You can't argue with success.