Bolt action 308 or 30-30 lever gun. Both will allow optics for hunting. The Mosin and SKS aren't readily designed for a scope without modification which would certainly put it over the $400 price point.
from personal experience. do not take on a mosin nagant. you will never be satisfied with the result unless you put a heck of a lot more than $400 into it. with some shopping around an SKS can be made into a pretty good sthf/hunting rifle. I've done it, perform a search on this forum for "SKS, poor mans EBR" and you will find a description of what I did to mine. mine it easily 2 MOA with tula and if I got match ammo would probably hold MOA.
Its too bad the internet wasn't around when my grandfather was alive. He would have been able to read about how he hunted with an inferior Mosin Nagant for his life after the Marine Corps. This rifle should not be discounted. Most are more than capable than the shooter behind them.
That said if you need one to double as a shtf rifle I would get a lever action. The Marlin 336 would fit the bill here. Good iron sights and a reliable action. Look for one with a JM stamp.
My younger brother took his first deer with an SKS using 124gr soft points. I would imagine it would also work fantastically as an SHTF rifle. As for making it yours, there is tons of aftermarket for the SKS.
The only problem I see is price, right now they are scarce for under $400, if you check armslist regularly you might find one in your area for cheap.
You're right Tucker, the SKS is still a underrated rifle by many. Too old, too heavy etc etc. I find them a lot of fun to shoot, cheap ammo and very capable of taking all kinds of game, as well as a good defensive weapon.
By the way, are you near Greeneville?
By all accounts they are accurate and reliable and only cost about $300 +/- depending where you buy. They are a compact semi-auto rifles that would work great for self defense and are in calibers that are easily come by including +p rounds. You can mount scopes and carry a higher capacity then most hunting rifles.