Run a live version of Voyager. I prefer Xfce over GNOME. They have many animated wallpaper install by default. You can look under the hood to see how they are doing it.
About Budgie first you should read the review about it on Distrowatch and see why it sucks. Kubuntu is a better bet but it will probably suffer from some of the same mistakes of Ubuntu being a rushed out release, full of incredible bugs and performance issues. Elementary has a good team behind it and the Pantheon desktop is indeed a work of art, showing amazing efficiency and simplicity, although I don't like it myself. I like to tweak my desktop to my own aesthetic standards and I love to do it, I think if I could I would be a "Graphical UI and OS Designer" myself. And that's why I use XFCE as my love of a lifetime desktop. It can be tweaked to beautiful perfection in a matter of hours from installation to finished product. Also I don't use Ubuntu based distros at all. I use Manjaro Linux, which in spite of being based on Arch Linux is incredibly stable (way more stable than Ubuntu LTS!) and also already beautiful out of the box. With a little love I tweaked it to look stunning, with all the elements of the OS integrated in the same designer concept. It always amazes me how people never think of XFCE as a beautiful desktop but that's because we have distros like Xubuntu that's plain ugly out of the box. Plus many more... Another alternative to you, if you really want to put up with Ubuntu bugs/performance problems would be Voyager. It's an Ubuntu LTS based distro that achieves what Xubuntu will never be able to and it's really beautiful out of the box. Take a look: https://voyagerlive.org/ I guarantee you that the first look at that page will make you want to know more.