OK, so I only know one person on here who makes AMVs, but still, this info is useful.
I just found a free download of some software that edits videos better than Windows Movie Maker. It's called VideoPad. I downloaded it, and although I haven't used it much, there are a lot of YouTube resources on how to use it. I haven't made any AMVs myself, but in theory I could if I knew how to rip a DVD.