I'm curious about the range you've chosen.
The small game I've hunted in the past with air rifles were taken at half of that range or less.
Most, if not all, of the game I hunted scurried for what they thought was a safe place.
There are different kinds.
The Benjamin 397
I haven't used this one in a long time. I think the one I did use was a 392 or something, though.
I don't know if it uses BBs or just pellets.
But it's a strong gun at 800 fps
(600 fps is the benchmark for hunting to me)
The Crosman 760
That was the one I used to hunt with the most.
I like the variable power of the pump action.
You don't always need full power for every shot and it saves wear on the cylinder seals.
Just makes the power range at 600 fps (10 pumps)
Dual ammunition with BBs and .177 pellets.
I bought a new
Daisy 880 but was not impressed with the quality of the plastic and the mechanism is a little fussy. Sometimes the gun won't fully cock and leave a dead trigger until you redo the load
The Crosman loads a magazine that allows you to pick out the BBs and ready the gun for pellets.
The Daisy, once loaded with BBs, chambers a ball on every cock, so it's a bit of a tedious effort to switch to pluck out the ball and use a pellet, especially if you're in a hurry to get off a second shot.
The BBs will take birds, squirrels and rabbits.
Pellets for raccoons.
I never shot at anything bigger than a coon.
The expected performance at longer range (and closer for coon size) is a disabling shot with a pellet and then a kill shot at closer range. Usually with a BB.
When my little brother was about 10, he hit a groundhog at 40 yards or better with a pellet from the Crosman.
It was either a great shot or a lucky one, but he hit it and the wound was severe enough to work.
I favor the Crosman 760 and would like to have the pellet pistol version
1377c as well.
If it's not dinner, it can be bait.