I have a Savage 116 in .270. While it is a good hunting rifle, it has never been as accurate as my Savage 110 in 7mm Remington Magnum (which is hyper-accurate with most loads).
My .270 is the least accurate with Remington Core-lokt loads (either 130 or 150 grain, but does seem to like the reduced-recoil variety). It seems to be the most accurate with plain Federal 130 grain Hi-shok bullets (right at 1" groups). I have been using Winchester 130 grain Silvertips in it for the past couple of years.
My 7mm is sub-MOA with Remington core-lokt, even though they represent the largest groups (just under 1"). The best has been with Winchester Supreme 150 grain BST (under 0.5 MOA).
Since every rifle is different, explore different brands and bullet styles over the years to come. Savage rifles due tend to be very accurate (some more than others though).