In my experience just about any inexpensive factory "deer ammo" shoots pretty well these days. Have had good luck with Federal blue box, Hornady American Whitetail, Remington Core-Lokt and Winchester Power Point.
The big problem may turn out not to be the ammo but the rifle's stock. Believe it or not, when the pre-'64 Featherweight was introduced in 1952, the forend was called "full floating," which meant free-floating. It lacked the forend screw that kept the barrel firmly connected to the stock, but also wasn't really free-floated (that happened with the post-'64 Model 70). As a result, the barrel often sort of rattled around in the forend, resulting in suck accuracy--what was common in the early reviews of pre-'64 Featherweights, which some reviewers attributed to the "too thin" barrel. The first Featherweights were all .308's, and some of the groups fired during a test by AMERICAN RIFLEMAN were over 4 inches, though some were around two. (Those were 5-shot groups, still the standard group-size for AR testing.) And since the pre-'64 stocks are made out of wood, they can warp slightly over time due to humidity.
There are ways to fix this if it occurs in your rifle. You can epoxy bed either the entire forend channel, or just the tip of the forend, providing a barrel-vibration damper like the "speed bump" still used in many factory stocks today,
Or you can place a plastic shim or two between the front of the action and the stock, just behind the recoil lug, really free-floating the barrel. This is what I did with an early .308 Featherweight purchased a couple years ago, whereupon it started shooting sub-inch groups. This technique has the advantage of not permanently altering an original rifle.
