I bought a VERY slightly-used Savage M116 in .338 last summer, this being the stainless-mit-synthetic version, and with a muzzle brake. It had fired exactly six rounds before it came to me.
Getting ready for an elk/whitetail hunt, I tried out the Barnes (handloaded) 225 TSX bullets for the first time, and found that this unmodified factory rifle will RELIABLY place three 225 TSX bullets in a group of less than 1/2" from 100 yards. It has a 3-9x Leupold scope mounted.
I killed a nice Alberta whitetail in fading light from 295 laser-ranged yards....one round, bang-flop.
I believe Savage rifles to be one of the great bargains of our day. They aren't fancy, but they DO SHOOT WELL. This is quite a concession, from one who greatly prefers blue steel and walnut. You have a very fine hunting rifle. The effective range is really determined by your own abilities, but for deer a bullet from the lighter end of the load selection probably should be used. There's also nothing wrong in picking a medium-weight bullet, like my 225s, and using it for everything you may hunt in North America.