What you're more likely to see happen is putting more money into a mediocre Mosin over the next year & ending up with...a mediocre long range shooter that could have been avoided if you would have waited another year & got a better platform right out the gate.
The Savage budget rifle shoots well, and the Ruger American I have personal experience with.
The Ruger, with a $150 Redfield scope on it, outshot at 100 yards a dedicated multi-thousand-dollar FBI sniper rifle. Ruger on a carpet-covered wooden box range rest, FBI gun on a bipod. Both on a concrete bench.
The Ruger in .30-06 can easily hold at one inch or less, even with its relatively flimsy stock. It shoots far more accurately for most buyers than it has a right to, at a very affordable price. Other calibers are reportedly running under an inch at 100 routinely.
It does not have sights, you WILL need to glass it, but the end result would be more in line with what the Remington 700 can do than taking a chance on a tight or loose bore in a Mosin & will have a much superior trigger to anything you can do with the FACTORY Mosin trigger.
Right now, surplus Mosin ammunition is cheap, but unless you luck out on a really good can, it is not long range stuff.
Any Mosin is a gamble; if you're determined to go with it because it's free, just understand what you're getting into.
Exercising patience & saving up for another year might save you both money AND aggravation.
Cheaping out due to impatience has caused a lot of regret in the gun world (and elsewhere).
In my case, a bunch of effort went into my sporter, but only as a toy. I already had better rifles & that Mosin will never be used for anything but play. If I were broke, had no other guns & looking for a cheap hunting rifle, I'd probably pick up a Mosin.
Looking to get into long range stuff, even on a budget, nope.
Good luck with your project.
Denis
Denis