If you have the option of variable chokes, I would go modified or improved with a 12 ga. It doesn't take much to kill cottontails. Snowshoes and jacks are another story. I have seen snowshoes and jacks run like the wind with a .22 through them and it doesn't slow them down much either. A .410 or a 28 ga will definately do the trick for you if you have one.

Emery