there's 2 different 22 "magnums" out there...take note. the 22WRF, sometimes referred to and mistaken as a "22 Magnum" is shorter than the 22WMR. WRF's can be fired out of a WMR, but you CANNOT fire WMR out of a WRF. Confused yet? I just don't want you to pick up a box of WRF thinking it's the same as WMR.
That said, on your savage, you are safe. It will fire both. Try out the Remington 33gr's and the CCI 40gr's first...i think you will like how one of them performs. Some folks have really good success out of the winchester 34's too...they do a number on small game.