The rule of thumb for me, as taught by my father and a plethora of his associates, is that rifles should be shot from a rested position. In the field, hunting, from a sitting or prone position, most generally. If you want to shoot standing, use a shotgun. For everyday shooting of my air rifles, I shoot from a bench. I would consider a bipod or tripod for informal plinking. What rocks my world is the smallest groups possible. Secondarily, when POA=POI. I'm generally able to do both, by adjustments of my scope.
While you have to do what rocks your own world, if you're shooting from an off-hand position, I believe you're gonna become greatly disappointed and frustrated with the world of air rifles. Personally, it doesn't bother me if I can't hit something while standing with a rifle, because that position is not in the real world for me! There are a LOT of guys who shoot off-hand, and are good at it. I'm not one of them, and don't care.
With all due respect, this might be something to consider. Shooting from a rested position doesn't have to be a ton of money invested at all.