RE: Good inexpensive scope
To answer your question logically, the answer is that you have the wrong set up for a cheap scope application.
It's kind of like buying a plow horse and then complaining about the feed bill.
There is a massive amount of recoil in a 300 Winchester Short Magnum.
You would have been better off buying a 270 / 30-06 type of rifle and then spending the money that you saved compared to theMagnumonA scope of your choice instead of spending all your money on the rifle and then not having a sufficient amount left over for a good quality scope.
Your rifles range- how far you can shoot accurately is determined by how good your scope is.
There is no one that I know ofthat is going to shoot 1000 yards at a 3 inch bulls eye with open sights.
Something as big as a buffalo - you didn't need a scope to shoot.
Even a monster 200 + lbs whitetail deer at 400 yards looks mighty small in a 9 power scope - through the woods - at first light and the last minutes before dusk. Normally the time when the big ones have a tendency to appear.
Re think your idea on a cheap scope and spends as much as you can - when you can afford it.
You still have a long time before most deer seasons begin with a rifle, 6 or more months in most places.
Surely - even if you just give up buying lottery tickets and coffee, you can save $20 a week, which would add up to$500 that you could use towards your purchase.