Before you do anything else....
Remove the scope base.
Clean the screw hole threads with a good solvent (acetone, etc.).
Clean the screws with the same solvent.
Clean any debris from the scope base and from the barrel.
Remount the base with Loctite 222 (purple) applied to the screw threads.
Then top it off with decent rings and your scope of choice.
If you don't check (and clean and remount) the base, it
will come loose on you.
And, I would skip the flash hider. There's no benefit for your use(s). A plain thread protector is a more sensible option.
If you want to shoot targets at close range with a suppressor it is a good choice. I'm not sold on it as a hunting round. With 125-150 gr bullets it is 400-500 fps slower than a 30-30. About 300 fps slower than 7.62X39
The problem is that big game bullets need a minimum of around 1800 fps in order to expand in game. You can't push bullets heavier than 150 gr fast enough at the muzzle and 150's are borderline even inside 100 yards. 125's will work at closer ranges, but once you get to a 125 gr 30 cal bullet there are better options.
A 77 gr 223 @ 2800 fps is a better big game killer.
I agree.
And, having recently been dealing with some cartridges that operate outside of the velocity windows typically associated with those calibers, I have come to better understand what a headache it can be to find a bullet that actually works.
(In my case, I'm dealing with 6mm bullets moving too slowly, .458" bullets moving too slowly, and .475" handgun bullets moving too quickly.)
If Mosin-Maurader is happy with the purchase, then that's great.
But, it's not the end-all-be-all hunting round that many people sell it as.
Case in point:
Terminal energy with a 110 gr bullet is nearly identical to .223 Remington with a 60 gr bullet, from 0 to 500 yards.
Short-range, it doesn't matter; but if you decide to try to go "long-range" (~250+ yd), .300 Blackout with a typical 110 gr bullet
drops twice as much as .223 Rem with a 60 gr bullet.