For varmints, over the years, I've had very good success with the 52/53gr boattail HP match bullets from Hornady and Sierra. Also any 55gr SP or HP, from all the major makers. However, pay attention to what you get, as some bullets (like the Hornady SX) have upper limits to the velocity.
Bullets meant to violently expand at 3000fps don't always do what you want at 36-3800fps.
Around here, before the bottom fell out of the coyote pelt market, the 40gr "Blitz" type bullet was very popular in the .22-250. Back when they first came out, dealers had a hard time keeping them on the shelf. The 40gr usually totally fragments inside a coyote, and (usually) doesn't exit. Only one hole in the hide is a plus to a fur hunter.
Not sure if it would do the same on fox, the smaller animal probably would have higher odds of an exit wound.
As to factory ammo, just about anybody's in the bullet weight you want will do fine, IF your particular rifle likes it. The difference between a 3/4in group and a 1.25in group isn't so critical at usual ranges for bigger varmints like fox, and up. Really small targets, or extreme ranges, then it might make the difference, but fox? probably not, depending on how you are hunting.