wee this is what I do for a living
It really really depends what form of animation your going for. A big thing going today for the arm-chair/ web content developer animator is flash. I will admit I don't touch that much but it's a growing form..
3D is a pretty simple form to get into, as there area plethora of cheap or free programs,( not counting those that one can obtain in less than legal forms) some of the more mainstream ones still to this day are Maya, and 3ds Max, both of which offer pretty decent demos " save for the watermarks"
Traditional hand drawn works in two ways now...one is to go traditional and use an animation stand and paper, draw it out there, copy it onto a cell, layer it under the camera, and shoot it in sets of 1-4 frames at a time depending on the speed you are looking for.. another option is to draw out the animations and scan them in frame by frame and assemble them in the PC using several various programs " can even be done on many many adobe programs)
Stop motion is one of the oldest and still popular forms, and I enjoy putting together little shorts for my boys now and then, and letting them help.. In the long run Stop motion is one of the easier forms as you have more direct control over multiple elements at once, and end up with a finished product with less clean up work in between and post like the other styles do.
so it really comes down to " what style your looking for"