The first question that you asked will give you really opinionated answers. Everyone has different viewpoints on what editing program is best. My personal favorite is Sony Vegas because it has a lot of different price options and is easier to learn than Adobe Premiere.
Here is a trial of the Sony Vegas Movie Studio version http://www.sonycreativesoftware.com/dow ... iestudiope
I don't know anything about windows live movie maker, but adding images and gifs should be the same as importing regular video. Here is a tutorial http://www.youtube.com/watch?v=3ZZij3NNyVg
But it should be noted that Windows Live Movie Maker isn't really a good editing program for AMVs. Its kinda like the lowest program on the video editing totem pole.