Hey, I'm an editor and used to do AMVs (I'd return to editing, but no time).
Anyways, what I do is play the video in VLC Media Player Classic and use FRAPS to screen record.
Files will be raw and quite large in file size, but that was never an issue for me as I had a 2TB drive dedicated to editing and project storage. Remember to disable subtitles when recording.
I used Sony Vegas Pro, After Effects CS5 & Photoshop CS5 to edit.
IMO, don't take TiYIER's advice.
Also, because you're starting fresh, you may want to watch some good AMVs and M@Ds to form your own unique editing style and so you know what to aim for. I recommend you watch these AMVs and get an idea of what you should try to do:
http://www.youtube.com/watch?v=HfjYsIeCLBMhttp://www.youtube.com/watch?v=KUFWjpYIZ8whttp://www.youtube.com/watch?v=GBY_KuH7QhUAll three AMVs (2nd one is a M@D) are completely different in style.
Don't expect too much on your first time, but please don't throw in a bunch of clips and music and call it an AMV. That's a disgrace and extreme eyesore for the rest of us editors.

If you need any further help editing, PM me

Ah and if you happen to find me on YT, my AMVs there aren't up to my current standards
