There are lots of aspects of creating cartoons and there are various products that help with different aspects.
Duik Tools for inverse kinematics and some other things
Auto Lip-Sync to animate the mouth of a character
iExpressions for inverse kinematics and other automation (I am currently preparing a comprehensive tutorial series for this, but for know, this tutorial will get you started: Puppet Animation with IK Expressions | mamoworld)
The next release of Creative Cloud will also include Adobe Character Animator, which will make many things easier and more fun. But currently, it is not yet available.
Mathias gave a great list for you to look into and I agree with his post.
If you know Flash I would also consider that as an option. There are a lot of character animation tricks and tips for animating characters in flash and then importing either the image sequence or .swf file into After Effects. I just finished a project using this process.