VHS:I dunno if this qualifies for the kind of software people are looking for but I had a great experience with this
vhs converter. I had the hardest time finding a software that would let me convert vhs tapes and let me edit the footage afterwards. I was originally going to use a conversion service where you send in your tapes and they send you back a dvd but they charged like $20/tape! It seems like you can try out the
converter for free for 30 days.
GIFs:
GIMP is always great to use. It's user-friendly and best of all it's free. I've heard a lot of people use photoshop but I don't really want to shell out the money just for making gifs ya know? Anyways, I absolutely recommend GIMP as well.
Media Player: VLC or MPLayer. Both have a built-in ffmpeg decoder so either is sufficient for me.
Video Editing: Still not sure if Final Cut Pro or Adobe after effects is better. I guess it depends on what you'd like to use it for (project-wise). FCP seemed more common within the business but now that seems to be shifting. Hollywood editors seem to vary with which they use so I say look at both and decide which fits your editing preferences more
I personally like FCP but that's what I started on so I might be biased...