At what distance are we talking about? I have a 17HRM that on a calm day will stack bullets at 100yds. I know a guy that says accuracy doesn't start till you are at 500yds! I shoot a contender pistol that I can shoot through the same hole at 50yds, at 100yds under an inch and at 200yds it will shoot four shots all on a 21/2" post-it, at 300yds the bullets really open up. On the same day I took my Remington 700 and out of a cold barrel, shot a 4 bullet group that all 4 bullet holes touched at 200yds. I am proud and pleased as punch with those two rifles, but that Contender is accurate!
I shoot a rifle well and a pistol, alright, better than most but not nearly as well as others. I think that unless something is wrong with the gun, all can shoot better than we are capable of.
I consider the minimum accuracy for varmint hunting to be what ever is required to kill your target with one shot. To be honest, I haven't met many people that shoot well or accurately over 200yds. I have seen some incrediblly accurate guns that can shoot exceedingly well with the right person behind them. I just have not seen that many gifted shooters. I do not consider myself to be a great shot, just alright, with alot to learn!
Qaz