Welcome to the pit! This is a fast and dirty guide not an exhaustive treatment.
The bog standard M-1891/30 rifle is your cheapest option. Sub $100 plus shipping and transfers from Gunbroker or AIM Surplus all day.
The M-189/30 is the basic issue rifle the USSR used against Hitler in the late unpleasantness of The Great Patriotic War.
Towards the end of the war the Soviets made a couple carbine versions, some conversions and some new built.
The M38 and M44 are the most common of those carbines and are distinguished by the folding bayonet. The M44 has a bayonet, the M38 don't. Prices seem to run between $150 and $400.
The rest of the Warsaw Pact and China issued them as well.
The nicest examples of the M44 are the Polish versions, some are new and unfired! Expect to spend a bit more for them though, $300-500.
Going back to rifles, the Finns made a nice one. The stock and sights are different and they've got a reputation for being shooters. $300-500 again, though.
If all you want is a $100 gun to mess with, get the 1891/30. It's hard to go wrong, really.
What you probably won't get is a tack-driving sniper rifle. The specifications for accuracy were rather loose by the standards of the day, the USSR was more concerned with it going bang every time. Some are excellent, some aren't and it's luck of the draw!
Changing out the stock will likely not help with anything, might be more comfortable to hold; but you're making a gun that kicks like a mule lighter. That's recoil enhancing! That will also add to barrel flip.
Be sure to get the bayonet! Many Mosins shoot BETTER with the thing mounted/extended. Mine does.
Originals of any variant except the Finn or snipers are cheap enough that you don't have to settle for a pre-bubba'd example to save money. Even if you want a bubba'd gun, best to start fresh.
Don't forget to check the bore! Remove the bolt and shine some light in there. Surplus 7.62x54mmR is corrosive and the typical conscript was not normally prompt about cleaning. Go ahead and be choosy about dark bores, there are plenty of nice shiny ones with crisp rifling out there for the same price.
Other than that, find one that you like the looks of. Quite a few were arsenal reworked at the end if the war and are relatively pristine today. Some show a lot of wear, but are still in good shape inside.
Have fun and good hunting!
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