The programming skills you're going to need apply to writing custom shaders (textures), physics models, and animation.
Luckily, since you're just starting, you won't need to get into any of that for awhile
What you need to do know is learn some software and some art. I assume you're focusing on 3D here, since most of the CG work done for broadcast is 3D. Discreet [http://www.discreet.com/index-nf.html
] develops a very nice modeling application called 3D Studio Max. It gets used a lot for broadcast work and game modeling. Another option would be to try Maya, by Alias/Wavefront [http://www.aliaswavefront.com/en/news/home.shtml
]. This is the package used on a great majority of movie work. It's touted as being the best, but is horribly expensive. For the free route you can check out Blender [http://www.blender3d.com/
], soon to be open source
, and PovRay [http://povray.org/
]. Neither can really compare to the comercial packages for easy of use and features, but they're certainly quality and are capable of awsome output. You might also look at Cinema4DL and AnimationMaster (I haven't used either).
Since you're targeting animation, you'll probably also need some compositing and post-production software. Adobe of course has some great tools for that (Photoshop, Premier, Aftereffects). the GIMP is also a good tool, and supposedly there is an animation module you can get for it, but you have to compile from source.