The short answer is that the right group and accuracy is the one
you are happy with.
Fur hunting/field conditions my view is:
First consider what would be the typical average distance at which you shoot your quarry.
Secondly what size killing zone are you looking at.
For example, a 3" group at 100 Yards with a deer caliber is absolutely fine - there is plenty of margin with a 6-8" killing zone. (Broadside h/l shots)
However a 2" Group at 50 yards is no good when trying to head-shoot rabbits with a .22Lr....
So having put things into perspective take a reality check and ignore all the comments about the importance of high precision accuracy. The reality, you will find, is that most stalkers do NOT achieve the 'clover-leave' and 'sub-1" group' at 100 yards they claim to achieve, even under controlled bench-rest conditions on a range. In real live hunting under field conditions we use sticks or a branch or a gate-post...and these wonderful groups of which some people even proudly post pictures are not achievable by most. What really matters is to
get as close to your quarry as you can and than to
humanely and safely dispatch it.
A now await many posts from people who tell you I am wrong and that your rifle and amo combe really, really should achieve a 5mm group at 100 yards or otherwise there must be something wrong with your kit or you

. Oh no there isn't...