I really like App-images. For the most part, they just work, download, run, done. And sometimes you want the flexibility to install something the distro’s pacakage manager doesn’t give you (or doesn’t have the latest version of). It’s a little extra work to put the app in system menus, etc though.
Package manger still preferred. Having the system deal with updates and dependencies is nice.
AUR is still good, but I’d take the App Image. Sometimes these work for me, sometimes they don’t. Still have to manually update them, AFAIK.
Ubuntu had a thing for a while where they would send you a CD if you asked for it. Friend of mine from school gave me one.