I know a guy in Kodiak that uses reduced loads (think .45 Colt levels) in his .458 Win Mag on bunnies.
He only has to carry one rifle for bunnies and bear protection. Keeps the magazine full of hot bear loads, and top loads in a light "bunny load" in after each shot. He doesn't miss often.
That being said, I recommend a .22lr above all others.
I used a 10/22 for a while, got bored with it, then used a Browning Buckmark pistol for the difficulty level to remain entertaining and challenging.
"To preserve liberty, it is essential that the whole body of the people always possess arms, and be taught alike, especially when young, how to use them." -Richard Henry Lee, Virginia delegate to the Continental Congress, initiator of the Declaration of Independence, and member of the first Senate, which passed the Bill of Rights.