For 3d animation, Animation: Master is, I understand, quite intuitive and easy to use, but I restricted my earlier suggestions to 2d software.

If you get into 3d, either with Blender or A:M or something else entirely, you'll have a somewhat bigger job, since you'll need more structure in the characters, you'll need to rig them, and you may need to do some work lighting and texturing. It's true that you get some things for free, and some people find 3d animation to be easier, but the set-up can take quite a bit longer.