As a former animator myself I'm going to butt in and make some suggestions.
Michael is correct in that what's the most important thing is to decide what approach you want and how much time you're willing to commit. Most TV animation is "limited". The Filmation style is what Warner Bros.' cartoon great Chuck Jones called "illustrated radio": there's so little animation (other than lip sync) that it is, for all practical purposes, still illustrations punctuated by moments of animation. If you're happy with this level of animation, then that's the level you should aim for...but don't underestimate how much work even that is.
Character animation is even more complicated, because it requires the characters to act primarily through their movements rather than relying on voice alone. This means body language and a myriad of expressions that require a real understanding of expressions and how to "pose" characters, and is vastly more work.
In either case, it's a good idea to understand as much about the subject as possible even if you decide to take the simplest approach. What I'm going to recommend are not related to software, but to animation theory and practices, specficially.
If you have a serious interest in the principles in animation, I recommend the book The Animator's Survival Kit
by animation master Richard Williams
(Who Framed Roger Rabbit). It totally demystifies the process, from the basics to advanced techniques.
A fun blog by a very opinionated animator who's worth reading even if you don't always agree with his tastes is that of Ren & Stimpy creator John Kricfalusi
, who discusses everything from layout to character appear to the downfalls of overly stylized characters.