I prefer a .22 short through the ear hole. It won't exit and you won't damage any fur there. Also there is normally less blood than with a .22 long. Can shoot em in a revolver and not have to use hearing protection which is nice.
Don't try to stand back and shoot through the cage, at least I never would. Some critters like to bounce all around in there, but be patient cause eventually they will give you a shot. Pick a spot to put the barrel up to the cage if they move around alot and wait .