Sounds like your mind is made up, but here are a couple things to consider.
If you a shooter and love your time on the range, get the Handi and you will have a fun project. If you are a hunter and would rather spend your free time in the field than reloading or testing loads, get the Stevens. Better yet, get one of each! Scoping the things is what costs the most, but with additional barrels, you will have to buy an extra scope anyway.
Follow up shots are not important unless you need one. Sooner or later, all hunters will. I am also a bowhunter, so I understand about making the first shot count!
Savages are known mostly for their accuracy. Others scoff at their looks, but not their accuracy. If you don't like the Stevens' plastic stock, it can always be replaced in the future with the same stocks made for Savage.
As far as long range shooting, you can do it with practice if the gun can. If the gun can't, you are whistling in the wind.
pepaw