If you really want to get into the guts of animation and media programming then Open Source IS the way to go. Ubuntu has a media version, there is Apodio which is a live CD
http://www.apodio.org/
Or there is the Live CD dyne:bolic
http://www.dynebolic.org
Actually the relevant programs are available for Windows, but first let's go into the alternative:
Autodesk owns two programs: Maya 3D and 3D Studio Max. Both use Pixar's proprietary Renderman protocols in their software so, they are somewhat expensive but they will give you a thoroughly professional product. For 2D the program most often used is Adobe's Flash -- most of the Youtube Videos are done with it and I recommend secretagentbob's Charlie the Unicorn videos as a good example.
Anyhow Blender was the in-house software for an Amsterdam Animation house in the early nineties. When it closed they open-sourced the project and ported it from (apparently) Unix to Windows and Mac OS X (if you have something on Unix it usually compiles on Linux without a problem so it was already there). Blender uses Linux: their Big Buck Bunny was rendered on a cluster farm of Ubuntu servers:
http://www.bigbuckbunny.org
http://www.blender.org
Anyhow, when you work on animation then you are talking about networks, and the three distros I mentioned on top have blender and lots of documentation on networking. They also have Synfig Studio which is an open source 2D animation program I DON'T LIKE. Don't use it. For fun you can try Pencil, http://www.pencil-animation.org and it's not finished but it's nowhere near as frustrating either.
Most Open Source software uses ImageMagick and ffmpeg or mplayer as backends. They are available across operating systems:
http://www.imagemagick.org
http://mplayerhq.hu
mplayer's page -- in Hungary -- is also where you go for information about ffmpeg.
There is also Avidemux. Which is a simple video editor. And it's worth mentioning here. It's one of the best out there. Look it up. It's also free.