ORIGINAL: Ridge Runner
The 300 has been killing deer and elk since 1920, can't argue with that, its a fine deer round, and always will be.
Now about the used 760, it could be a gem ya never know, where is the sling swivel mounted? if mounted to the barrel it would be ok, but if mounted to the forearm ya better check it out good. the screw mounted swivel on the end of the forearm gradualy over time warps the slide bars from the weight of the rifle pulling on them from carrying the rifle slung over the shoulder. my own 1979 vintage 760 in 270 win suffered this and what happens is the action will sporaticly not lock shut. The lever that locks them is all the way up so the trigger will pull but its possible that the rifle will fire out of battery (bolt not fully closed) causing a catostrophic failure (busted case). they can be fixed but its something to look at.
RR
All of the model 760 300 Sav. were made with the original style mounting which had a lug brazed to the barrelthat held the end of the slidetube. This was a very solid connection and it was typical for gunsmiths of the day to tap and drill the end cap of the slide tube for a swivel stud. They never gave problems. In the mid 60's Remington, beginning with the BDL models,changed this connection to the free floating tube. Swivels mounted to the end of the forearms of these models gave the problems you mentioned.