I dunno about the best, but I use GIMP (which is also a pretty good free art software in general).
This is probably my 7th best example of animating with GIMP because the other 6 ones are secret.
But if you're just starting out I would actually recommend using this website:
http://gifcreator.me/
The important thing to know about animating is that there is no magic software that makes you good at animating. If you want to make a good animation, you'll want to draw every single frame yourself.
Rather than getting bogged down with any complicated settings, you should first learn the basics of animating which is just drawing a bunch of similar pictures with small differences and showing each one to your audience really quickly in a certain order. The website I recommend if you're just starting out just makes gifs so you can choose whatever software you use to make your frames and is pretty simple to use and make animated gifs with.